Question

B) The point B divides AC in the ratio 2 : 3.

Work out vector OC in terms of a and b.
Simplify your answer.
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Answer 1

c = (5b -3a)/2

Explanation:

You want to find vector OC in terms of 'a' and 'b', given that B divides AC in the ratio 2 : 3.

Solution

The point B satisfies ...

B = (2C +3A)/5

Solving for C gives ...

5B -3A = 2C

C = (5B -3A)/2

In terms of the vectors a = OA, b = OB, this is ...

c = (5b -3a)/2