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Get all the right understanding on Class 12 Three Dimensional Geometry

Class 12 Three Dimensional Geometry is one of the most important chapters. In order to make sure that the students get the right understanding, the experts of Doubtnut has prepared the best study material that proves to be of much help to the students.<br><br>For more such video solutions/Pdf solutions, visit doubtnut.com and clear your doubt instantly.

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Get all the right understanding on Class 12 Three Dimensional Geometry

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  1. JEE CONCEPTS BOOSTER THREE DIMENSIONAL GEOMETRY  Download Doubtnut Today Ques No. Question CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 1. INTRODUCTION 1 1. Coordinates of point in space; sign of coordinates of a point  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 1. INTRODUCTION 2 2. Distance formula in 3D  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 1. INTRODUCTION 3 3. Section formula (internal + external)  Click to LEARN this concept/topic on Doubtnut

  2. CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 1. INTRODUCTION 4 4. The x coordinates of a point on the line joining the points Q(2; 2; 1) and R(5; 1; -2) is 4. Find its z coordinate.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 2. DIRECTION COSINES AND DIRECTION RATIOS 5 1. Direction cosine and ratio of line  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 2. DIRECTION COSINES AND DIRECTION RATIOS 6 2. Direction Ratio of line along the bisector of two given lines  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 2. DIRECTION COSINES AND DIRECTION RATIOS 7 3. Find the distance of the point P(a; b; c) from the x axis  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 3. ANGLE BETWEEN TWO LINES 8 1. Angle Between Two vectors in terms of direction cosine and direction ratio  Click to LEARN this concept/topic on Doubtnut

  3. CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 3. ANGLE BETWEEN TWO LINES 9 2. Condition of parallel and perpendicular lines  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 3. ANGLE BETWEEN TWO LINES 3. Find the angle between the lines whose direction cosines are given by the equations 3l + m + 5n = 0 and 6mn − 2nl + 5lm 10 = 0  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 3. ANGLE BETWEEN TWO LINES 11 4. Angle between line if relation between direction cosine is given  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 3. ANGLE BETWEEN TWO LINES 12 5. Angle between two lines in vector and cartesian form  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY

  4. 3. ANGLE BETWEEN TWO LINES 13 6. Equation of line passing through a given point and parallel to given line  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 3. ANGLE BETWEEN TWO LINES 14 7. Equation of line passing through a given point and perpendicular to given line  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 3. ANGLE BETWEEN TWO LINES 15 8. Perpendicularity of two lines  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 3. ANGLE BETWEEN TWO LINES 16 9. Find the equation of a line parallel to x axis and passing through the origin.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 3. ANGLE BETWEEN TWO LINES 10. Find the angle between the lines; one of which has direction ratios 2;2;1 while the other one is obtained by joining the points (3; 1; 4) and (7; 2; 12). 17  Click to LEARN this concept/topic on Doubtnut

  5. CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 4. EQUATION OF LINE PASSING THROUGH TWO GIVEN POINT 18 1. Vector and cartesian equation of line  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 4. EQUATION OF LINE PASSING THROUGH TWO GIVEN POINT 19 2. Reduction of cartesian form of a line to vector form and vice versa  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 4. EQUATION OF LINE PASSING THROUGH TWO GIVEN POINT 3. Find the vector equation of the line through A(3; 4; -7) and B(1; -1; 6). Find also; its cartesian equation. 20  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 4. EQUATION OF LINE PASSING THROUGH TWO GIVEN POINT 21 4. Collinearity of three points  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 5. INTERSECTION OF TWO LINES 22 1. Algorithm for intersection of two lines

  6.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 5. INTERSECTION OF TWO LINES 23 2. Conditions for line to intersect  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 6. PERPENDICULAR DISTANCE OF A POINT FROM A LINE 24 1. Perpendicular distance of a point from line in vector and cartesian form  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 7. SHORTEST DISTANCE BETWEEN TWO STARIGHT LINES 25 1. Shortest distance between two skew lines in vector + cartesian form  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 7. SHORTEST DISTANCE BETWEEN TWO STARIGHT LINES 26 2. Shortest distance between two parallel lines in vector + cartesian form  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 7. SHORTEST DISTANCE BETWEEN TWO STARIGHT LINES

  7. 27 3. Calculation of shortest distance when one in symmetric form amd other in unsymmetric form  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 28 1. Equation of plane (vector and cartesian form) in point normal form  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 29 2. Equation of plane passing through 3 points in vector + cartesian  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 30 3. Proving coplanarity of four points  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 31 4. Intercept form of a plane  Click to LEARN this concept/topic on Doubtnut

  8. CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 5. Equation of plane passing through given point and normal to given vector 32  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 6. Write the equation of the plane whose intercepts on the coordinate axes are -4; 2 and 3 respectively. 33  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 34 7. Equation of plane passes through a point and perpendicular to two given planes  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 35 8. Equation of plane passing through two points and perpendicular to a plane

  9.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 9. Equation of plane passes through a point and parallel to two given lines (parametric form) 36  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 10. Equation of plane passes through a point and parallel to two given lines(non parametric form 37  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 38 11. Equation of a plane parallel to a given plane(vector + cartesian)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 8. PLANE 39 12. Equation of a plane passing through a point and perpendicular to the line  Click to LEARN this concept/topic on Doubtnut

  10. CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 9. ANGLE BETWEEN TWO PLANES 40 1. Angle between two planes  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 10. DISTANCE BETWEEN PLANE 41 1. Distance between two parallel planes  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 11. DISTANCE BETWEEN PARALLEL PLANES 1. Equation of plane parallel to a given plane at some distance 42  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 11. DISTANCE BETWEEN PARALLEL PLANES 43 2. Equation of plane passing through intersection of two planes and given point  Click to LEARN this concept/topic on Doubtnut

  11. CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 11. DISTANCE BETWEEN PARALLEL PLANES 44 3. Problems on equation of plane passing through intersection of two planes  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 12. DISTANCE OF A POINT FROM A PLANE 45 1. Distance of a point from plane (vector + cartesian)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 12. DISTANCE OF A POINT FROM A PLANE 46 2. Distance of a point from plane measured parallel to a line  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 13. IMAGE OF POINT (REFLECTION) 47 1. Mirror image of a point in plane  Click to LEARN this concept/topic on Doubtnut

  12. CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 13. IMAGE OF POINT (REFLECTION) 48 2. Mirror image of a line in plane  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 14. LINE AND PLANE 49 1. Reduction of unsymmetrical form of line into symmetrical form  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 15. ANGLE BETWEEN LINE AND PLANE 50 1. Angle between line and plane  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 16. ANGLE BETWEEN A LINE AND A PLANE 51 1. Equation of plane passes through two points and parallel to a line  Click to LEARN this concept/topic on Doubtnut

  13. CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 17. INTERSECTION POINT OF LINE AND PLANE 52 1. Intersection of a line and plane  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 18. CONDITION FOR A LINE TO LIE IN A PLANE 53 1. Condition for a line to lie in a plane  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 18. CONDITION FOR A LINE TO LIE IN A PLANE 54 2. Condition of coplanarity of two lines and equation of the plane containing them  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 19. DISTANCE BETWEEN SKEW LINES 1. Alternate method for shortest distance calculation for skew lines 55  Click to LEARN this concept/topic on Doubtnut

  14. CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 20. EQUATION OF A PLANE BISECTING THE ANGLE BETWEEN TWO PLANES 1. Equation of Plane Bisecting the angle between two planes in vector and cartesian form 56  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 20. EQUATION OF A PLANE BISECTING THE ANGLE BETWEEN TWO PLANES 57 2. Bisector of the plane containing origin  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 20. EQUATION OF A PLANE BISECTING THE ANGLE BETWEEN TWO PLANES 58 3. Bisector of plane (acute/obtuse bisector)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 21. POSITION OF POINT WRT PLANE 59 1. Position of point wrt to plane  Click to LEARN this concept/topic on Doubtnut

  15. CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 22. FAMILY OF PLANES 1. Find the equation of a plane containing the line of intersection of the planes x + y + z − 6 = 0 and 2x + 3y + 4z + 5 60 = 0 and passing through (1, 1, 1)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 22. FAMILY OF PLANES 2. Find the distance between the parallel planes x + 2y − 2z + 1 = 0 and 2x + 4y − 4z + 5 61 = 0  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR JEE || Chapter THREE DIMENSIONAL GEOMETRY 23. EQUATION OF SPHERE 62 1. EQUATION OF SPHERE  Click to LEARN this concept/topic on Doubtnut  Download Doubtnut to Ask Any Math Question By just a click  Get A Video Solution For Free in Seconds  Doubtnut Has More Than 1 Lakh Video Solutions  Free Video Solutions of NCERT, RD Sharma, RS Aggarwal, Cengage (G.Tewani), Resonance DPP, Allen, Bansal, FIITJEE, Akash, Narayana, VidyaMandir

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