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2 marksSimplifying Vector Expressions

CSEC Mathematics · Question 10(b)(ii)

Relative to the origin O(0, 0), the position vectors of points A and B are OA = [9; 0] and OB = [3; 6] respectively. Points D and E are on AB and OA respectively, such that AD = (1/3)AB and OE = (1/3)OA. A diagram illustrates this information.

Express the vector OD in the form [a; b].

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Other parts of this question

  1. 10(a)(i)a)Find the matrix product [-1 3; 4 h] [k; 5].[2 marks]
  2. 10(a)(i)b)Hence, find the values of h and k that satisfy the matrix equation [-1 3; 4 h] [k; 5] = [0; 0].[2 marks]
  3. 10(a)(ii)Using a matrix method, solve the simultaneous equations 2x + 3y = 5 and -5x + y = 13.[3 marks]
  4. 10(b)(i)Express the vector AB in the form [a; b].[1 mark]
  5. 10(b)(iii)Express the vector BE in the form [a; b].[2 marks]

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