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Question

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


Your Answer
A
2a3b
Your Answer
B
3a2b
Correct Answer
C
3b2a
Your Answer
D
2b3a

Solution

The correct option is D 3b2a

It is given in the question that AC=3AB
BC=ACAB
BC=3ABAB       (AC=3AB)
BC=2AB
Now ACBC=|AC||BC|=|3AB||2AB|=32|AB||AB|=32
So C divides AB in the ratio 3:2 externally.
And we know that position vector of point P dividing AB externally in the ratio m:n is given by mBnAmn
Therefore the position vector of C is given by,
r=3b2a32=3b2a, which is the correct answer.

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