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Question

If a and b are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that AC=3AB is ______________________.

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Solution

Given:
AC=3AB


Let c is the position vectors of C.

AC=3ABc-a=3b-ac-a=3b-3ac=3b-3a+ac=3b-2a


Hence, If a and b are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that AC=3AB is 3b-2a.

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