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Vectors

Vectors. A VECTOR?. Describes the motion of an object A Vector comprises Direction Magnitude We will consider Column Vectors General Vectors Vector Geometry. Size. NOTE! Label is in BOLD . When handwritten, draw a wavy line under the label i.e. a. Column Vectors. Vector a.

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Vectors

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  1. Vectors

  2. A VECTOR? • Describes the motion of an object • A Vector comprises • Direction • Magnitude • We will consider • Column Vectors • General Vectors • Vector Geometry Size

  3. NOTE! Label is in BOLD. When handwritten, draw a wavy line under the label i.e. a Column Vectors Vector a 2 up 4 RIGHT COLUMN Vector

  4. b Column Vectors Vector b 2 up 3 LEFT COLUMN Vector?

  5. n Column Vectors Vector u 2 down 4 LEFT COLUMN Vector?

  6. b a d c Describe these vectors

  7. Alternative labelling F B D E G C A H

  8. k k k k General Vectors A Vector has BOTH a Length & a Direction All 4 Vectors here are EQUAL in Length and Travel in SAME Direction. All called k k can be in any position

  9. k General Vectors Line CD is Parallel to AB B CD is TWICE length of AB D A 2k Line EF is Parallel to AB E EF is equal in length to AB C -k EF is opposite direction to AB F

  10. k Write these Vectors in terms of k B D 2k F G ½k 1½k E C -2k A H

  11. B k D A C Combining Column Vectors

  12. C B A Simple combinations

  13. Q P R a b O Vector Geometry Consider this parallelogram Opposite sides are Parallel OQ is known as the resultant of a and b

  14. Resultant of Two Vectors • Is the same, no matter which route is followed • Use this to find vectors in geometrical figures

  15. . Q S S is the Midpoint of PQ. Work out the vector P R a b O Example = a + ½b

  16. . Q S S is the Midpoint of PQ. Work out the vector P R a b O Alternatively - ½b = b + a = ½b + a = a + ½b

  17. C p M Find BC = + A q B BC BA AC AC= p, AB = q Example M is the Midpoint of BC = -q + p = p - q

  18. C p M Find BM = ½BC A q B BM AC= p, AB = q Example M is the Midpoint of BC = ½(p – q)

  19. C p M Find AM + ½BC = A q B AM AB AC= p, AB = q Example M is the Midpoint of BC = q + ½(p – q) = q +½p - ½q = ½q +½p = ½(q + p) = ½(p + q)

  20. C p M Find AM + ½CB = A q B AC AM AC= p, AB = q Alternatively M is the Midpoint of BC = p + ½(q – p) = p +½q - ½p = ½p +½q = ½(p + q)

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