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Vectors

P. A. a. N. O. b. B. Q. Vectors. Express each of the following vectors in terms of a , b or a and b. Example In the diagram, OA = AP and BQ = 3OB. N is the midpoint of PQ. and. (a) (b) (c) (d) (e) (f) (g) (h).

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Vectors

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  1. P A a N O b B Q Vectors Express each of the following vectors in terms of a, b or a and b. Example In the diagram, OA = AP and BQ = 3OB. N is the midpoint of PQ. and (a) (b) (c) (d) (e) (f) (g) (h)

  2. Example ABCDEF is a regular hexagon with , representing the vector m and , representing the vector n. Find the vector representing

  3. A C D a E O b B Example In the diagram, and , OC = CA, OB = BE and BD : DA = 1 : 2. • a) Express in terms of a and b • (i) • b) Explain why points C, D and E lie on a straight line.

  4. Example ABC is a triangle with D the midpoint of BC and E a point on AC such that AE : EC = 2 : 1. Prove that the sum of the vectors , , is parallel to

  5. Example OABC is a quadrilateral.M, N, P and Q are the mid-points of OA, OB, AC and BC. OA = a, OB = b, OC = c (a) Find, in terms of a, b and c expressions for (i) (ii) (iii) (b) What can you deduce about the quadrilateral MNQP?

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