Find the best JEE Concepts on Vector Algebra of Class 12

1. JEE CONCEPTS BOOSTER VECTOR ALGEBRA  Download Doubtnut Today Ques No. Question CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 1. INTRODUCTION 1 1. Two type of numbers - Vector and scalar.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 2. EVOLUTION OF VECTOR CONCEPT 2 1. Evolution of vector concept  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 2. EVOLUTION OF VECTOR CONCEPT 3 2. Representation of vector direction sense magnitude of vector or length  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 3. TYPES OF VECTORS

2. 4 1. Equal vectors, null vector, unit vectors, position vector, like and unlike vectors,collinear and parallel vectors  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 3. TYPES OF VECTORS 2. Co-initial vectors, coterminous vector and co-planar vectors,negative of a vector,reciprocal vectors 5  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 3. TYPES OF VECTORS 6 3. Free vector and localized vector  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 3. TYPES OF VECTORS 4. In a regular hexagon find which vectors are collinear, equal, coinitial, collinear but not equal. 7  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 4. ADDITION OF VECTOR 8 1. Parallelogram law of addition of vectors  Click to LEARN this concept/topic on Doubtnut

3. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 4. ADDITION OF VECTOR 9 2. Properties of addition of vectors  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 4. ADDITION OF VECTOR 10 3. Magnitude of addition of two vectors  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 4. ADDITION OF VECTOR 11 4. Commutative law  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 4. ADDITION OF VECTOR 12 5. Associative law  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 4. ADDITION OF VECTOR 13 6. Existence of additive identity  Click to LEARN this concept/topic on Doubtnut

4. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 4. ADDITION OF VECTOR 14 7. Existence of additive inverse  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 4. ADDITION OF VECTOR 8. ABC is a triangle and P any point on BC. If show that is a parallelogram and ABQC is the sum of therefore; is a fixed point. ; 15 ¯ ¯ ¯ P Q ¯ ¯ ¯ A P +¯ ¯ ¯ P B +¯ ¯ ¯ P C Q  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 4. ADDITION OF VECTOR 16 9. Addition of vectors in 3 dimensional space  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 4. ADDITION OF VECTOR 10. ABCD is a parallelogram. E; F are mid point of BC; CD respectively. AE; AF meet the diagonal BD at points Q and P respectively. Show that points P and Q trisect DB. 17  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 5. COMPONENTS OF A VECTOR

5. 18 1. Component of vector  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 6. MULTIPLICATION OF A VECTOR BY A SCALAR 19 1. Definition geometric interpretation: Multiplication Of A Vector By A Scalar  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 6. MULTIPLICATION OF A VECTOR BY A SCALAR 20 2. Properties of Multiplication of a vector by a scalar  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 7. POSITION VECTOR OF A POINT 21 1. Position vector and a vector in terms of position vectors of its end points  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 8. SECTION FORMULA 22 1. Section formulae (Internal division)  Click to LEARN this concept/topic on Doubtnut

6. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 8. SECTION FORMULA 23 2. Section formula (External division)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 8. SECTION FORMULA are the position vectors of A and B respectively; find the position → 24 → 3. If vector of a point C on BA produced such that BC = 3/2 BA. a b and  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 25 1. Definition and physical interpretation: Linear Combination  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 26 2. Linear Combination: Linear Independence And Linear Dependence  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 27 3. Linearly Independent

7.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 28 4. Linearly Dependent  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE are two non collinear vectors; then every vector → b → a → r 5. Theorem 1: If and → b → b 29 and → a → a coplanar with can be expressed in one and only one way as a linear combination: x +y .  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE → b → a are non coplanar vectors; then any vector → c → a → b → c can be → r 6. Theorem 2: If , and 30 expressed as linear combination: x +y +z  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE → b → b→ 31 → a → c → a 7. Theorem 3:If vectors , and are coplanar then det( ) = 0 c  Click to LEARN this concept/topic on Doubtnut

8. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 8. Examples: Prove that the segment joining the middle points of two non parallel sides of a trapezium is parallel to the parallel sides and half of their sum. 32  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 33 9. Components of a vector in terms of coordinates of its end points  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 34 10. Subtraction of vectors in terms of its components  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 11. The lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent. 35  Click to LEARN this concept/topic on Doubtnut

9. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 36 12. Collinearity for more than two points  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 37 13. Multiplication of a vector by a scalar in terms of components  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 38 14. Equality of vectors in terms of components  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 15. Show that the three points A( − 2,3,5); 39 B(1, 2, 3) and are collinear. C(7, 0, − 1)  Click to LEARN this concept/topic on Doubtnut

10. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 16. If (2,0,0); (0, 1, 0); have position vectors A; B;C 40 (0,0,2) Show that triangle ABC is isosceles.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 9. LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE 41 17. Find the unit vector in the direction of 3i − 6j + 2k  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 10. VECTOR JONING TWO POINTS 42 1. Position vector in 2 dimensional plane and 3 dimensional plane  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 10. VECTOR JONING TWO POINTS 43 2. Components of vector joining two point in 2 and 3 dimensional plane  Click to LEARN this concept/topic on Doubtnut

11. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 11. DIRECTION COSINES AND DIRECTION RATIOS 44 1. Direction cosines  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 11. DIRECTION COSINES AND DIRECTION RATIOS 45 2. Direction ratios  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 11. DIRECTION COSINES AND DIRECTION RATIOS 46 3. Direction cosines of of a vector  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 11. DIRECTION COSINES AND DIRECTION RATIOS 47 4. Direction ratio of the line segment joining two points  Click to LEARN this concept/topic on Doubtnut

12. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 11. DIRECTION COSINES AND DIRECTION RATIOS 5. Two parallel vectors have proportional direction ratios and representation of vector in terms of direction ratios. r 48  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 11. DIRECTION COSINES AND DIRECTION RATIOS 49 6. Projection of vector along coordinate axes; if direction cosine is given  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 12. DOT PRODUCT 50 1. Definition; remarks and geometrical interpretation of Scalar Product  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 13. PROPERTIES OF DOT PRODUCT 51 a.a = |a|2 1. and commutative and distributive law of dot product  Click to LEARN this concept/topic on Doubtnut

13. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 13. PROPERTIES OF DOT PRODUCT 2. l→ a .m→ b = lm(→ a 52 .→ b ) → a .→ are perpendicular if → b → b → a → a and then and and are not null vector b = 0  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 13. PROPERTIES OF DOT PRODUCT 3. 2 → a ±→ 2 → a∣∣ ∣∣∣ b∣∣∣ =∣∣ 2 → b∣∣∣ +∣∣∣ → b∣∣∣cosθ ± 2∣∣→ a∣∣∣∣∣ 53 and a +→ (→ b ) a −→ 2 .(→ → a∣∣ b ) =∣∣ 2 → b∣∣∣ −∣∣∣  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA

14. 13. PROPERTIES OF DOT PRODUCT 54 4. Dot product in terms of components  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 13. PROPERTIES OF DOT PRODUCT 5. Using dot product of vectors; prove that a parallelogram; whose diagonal are equal; is a rectangle. 55  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 14. APPLICATIONS OF DOT (SCALAR) PRODUCT 56 1. Angle between two vectors in terms of dot product  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 14. APPLICATIONS OF DOT (SCALAR) PRODUCT 57 2. Components of vector along and perpendicular a vector  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 14. APPLICATIONS OF DOT (SCALAR) PRODUCT 58 3. Cosine rule using dot product  Click to LEARN this concept/topic on Doubtnut

15. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 14. APPLICATIONS OF DOT (SCALAR) PRODUCT 4. Prove by vector method that cos(A + B) 59 = cosAcosB − sinAsinB  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 15. VECTOR (OR CROSS) PRODUCT OF TWO VECTORS 60 1. Definition and meaning of cross product  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 15. VECTOR (OR CROSS) PRODUCT OF TWO VECTORS 61 2. geometrical interpretation of cross product and area of parallelogram  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 15. VECTOR (OR CROSS) PRODUCT OF TWO VECTORS 62 3. Vector product: Determinant form  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA

16. 15. VECTOR (OR CROSS) PRODUCT OF TWO VECTORS 63 → b → a 4. Vector normal to the plane; passing through and  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 15. VECTOR (OR CROSS) PRODUCT OF TWO VECTORS 64 5. The area of parallelogram; triangle and quadrilateral in terms of cross product.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 15. VECTOR (OR CROSS) PRODUCT OF TWO VECTORS → a ;→ 6. Lagrange identity: If two vector a ×→ b∣∣∣ are any two vectors b 2 → ∣∣∣ 2 → b∣∣∣ 65 2∣∣∣ → a∣∣ = (∣∣ 2 a .→ − (→ ) b )  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 15. VECTOR (OR CROSS) PRODUCT OF TWO VECTORS a −→ a +→ → b ) (→ b ) (→ b ) = 2(→ 66 7. Show that x x a

17.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 15. VECTOR (OR CROSS) PRODUCT OF TWO VECTORS 67 8. Application of cross product trigonometric proof; sin(A+B) = sinAcosB + cosAsinB  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 16. PROPERTIES OF CROSS PRODUCT 68 1. Non commutative and distributive law of vector product  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 17. SCALAR TRIPLE PRODUCT 69 1. Introduction and definition of Scalar triple product  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 17. SCALAR TRIPLE PRODUCT 70 2. Geometrical interpretation of Scalar triple product and volume of parallelepiped  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 17. SCALAR TRIPLE PRODUCT

18. 71 3. Coplanarity of points  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 17. SCALAR TRIPLE PRODUCT 4. Find , for which the points a A(3, 2,1), 72 B(4, a,5), C(4, 2, − 2) and are coplanar. D(6,5, − 1)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 17. SCALAR TRIPLE PRODUCT 73 5. Find [l m n][a b c]  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 17. SCALAR TRIPLE PRODUCT 74 6. Volume of tetrahedron and parallelepiped  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 18. PROPERTIES OF SCALAR TRIPLE PRODUCT

19. 75 1. Property 1: Position of the dot and cross can be interchanged without altering the product.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 18. PROPERTIES OF SCALAR TRIPLE PRODUCT 2. Property 2: → b [k→ → c] 76 a → b = k[→ → c] a  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 18. PROPERTIES OF SCALAR TRIPLE PRODUCT 3. Property 3&4: a +→ → d] [→ → c b 77 → d] = [→ → c a + [→ → d] → b and right and left handed system c  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 18. PROPERTIES OF SCALAR TRIPLE PRODUCT 4. Property 5-7: Box product of coplanar vector is 0 and box product of → a ,→ a and → b 78 is 0 and box product in terms of determinant.

20.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 18. PROPERTIES OF SCALAR TRIPLE PRODUCT 79 5. Property 8: Distributivity of vector product over vector addition  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 18. PROPERTIES OF SCALAR TRIPLE PRODUCT → a ,→ b ,→ 6. For any three vectors a +→ b find c 80 → b +→ [→ a] → c +→ c  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 18. PROPERTIES OF SCALAR TRIPLE PRODUCT 7. Simplify a −→ 81 → b −→ [→ a] → c −→ b c  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 18. PROPERTIES OF SCALAR TRIPLE PRODUCT 82 8. Evaluate . Also, interpret it geometrically. [i j k]

21.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 19. VECTOR TRIPLE PRODUT 1. Prove that ˆi × (→ a ×→ i ) +ˆj a ×→ × (→ j ) +ˆk 83 a ×→ × (→ k ) = 2→ a  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 19. VECTOR TRIPLE PRODUT → b ).(→ → d ) =→ a .(→ → d )) 84 (→ (→ 2. Lagrange identity: x x x x a c b c  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 20. RECIPROCAL SYSTEM OF VECTORS 1. Definition & Property 1: → a .→ a ' = → b .→ c .→ ' = 1 85 b ' =→  Click to LEARN this concept/topic on Doubtnut

22. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 20. RECIPROCAL SYSTEM OF VECTORS 2. Property 2 & 3: → a .→ b ' =→ → b .→ c ' =→ a .→ c ' c .→ = a ' and = 0 86 → b [→ → c] a → b ' [→ → c '] a ' = 1  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 20. RECIPROCAL SYSTEM OF VECTORS 87 3. Property 4: The orthogonal triad of vectors is self reciprocal. ˆi,ˆj,ˆk  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 20. RECIPROCAL SYSTEM OF VECTORS → a ,→ → a ',→ → c → c ' 4. Property 5: Vectors are non-coplanar. and are non-coplanar iff vectors and 88 b ' b  Click to LEARN this concept/topic on Doubtnut

23. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 21. MISCELLANEOUS 1. Find ˆi × (→ a ׈i) +ˆj 89 × (→ a ׈j) +ˆk × (→ a ׈k)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 21. MISCELLANEOUS → a ,→ → c 2. Let and be any three vectors; then prove that b 90 2 a ×→ → b ×→ → b [→ a] = [→ → c] → c ×→ b c a  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 21. MISCELLANEOUS → a ,→ are three non-coplanar vectors and r is any arbitrary vector. Prove → c 3. that [→ and b → r]→ → c a b → r]→ 91 + [→ → a b c → r]→ → b + [→ c a → c]→ → b = [→ r a  Click to LEARN this concept/topic on Doubtnut

24. CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 21. MISCELLANEOUS 4. Find the volume of a parallelopiped having three coterminus vectors of equal ∣∣ a∣∣ θ 92 → magnitude and equal inclination with each other.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 22. SUBTRACTION OF VECTORS 93 1. Subtraction of vectors  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 22. SUBTRACTION OF VECTORS 2. If sum of two unit vectors is a unit vector; prove that the magnitude of their difference is √3 94  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter VECTOR ALGEBRA 22. SUBTRACTION OF VECTORS 3. Let O be the centre of a regular hexagon ABCDEF. Find the sum of the vectors , and OB, OC,OD, OE OF 95 OA  Click to LEARN this concept/topic on Doubtnut  Download Doubtnut to Ask Any Math Question By just a click

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