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If three points A,B and C are collinear,...

If three points A,B and C are collinear, whose position vectors are `hati-2hatj-8hatk,5hati-2hatk and 11hati+3hatj+7hatk` respectively, then the ratio in which B divides AC is

A

A. `1:2`

B

B. `2:3`

C

C. `2:1`

D

D. `1:1`

Text Solution

Verified by Experts

The correct Answer is:
B
Let the B divide AC in ratio `lamda:1` then
`5hati-2hatk=(lamda(11hati+3hatj+7hatk)+hati-2hatj-8hatk)/(lamda+1)`
`implies 3 lamda-2=0`
`implies lamda=(2)/(3),` i.e., ratio`=2:3`.
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