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If a,b are the position vectors of A,B r...

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

A

`3a-b`

B

`3b-a`

C

`3a-2b`

D

`3b-2a`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, given that AC=3AB. It means that point C divides AB externally.
Thus, `AC:BC=3:2`

Hence, `OC=(3*b-2*a)/(3-2)=3b-2a`
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