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If the position vectors of A,B,C and D a...

If the position vectors of A,B,C and D are
`2hati+hatj,hati-3hatj,3hati+2hatj and hati+lamda hatj` respectively and `vec(AB)||vec(CD)`. Then `lamda` will be

A

`-8`

B

`-6`

C

8

D

6

Text Solution

Verified by Experts

The correct Answer is:
B
`AB=(hati-3hatj)-(2hati+hatj)=-hati-4hatj`.
`CD=(hati+lamdahatj)-(3hati+2hatj)=-2hati+(lamda-2)hatj`
`AB||CDimpliesAB=xCD`
`-hati-4hatj=x{-2hati+(lamda-2)hatj}`
`implies -1=-2x,-4=(lamda-2)x`
`impliesx=(1)/(2) and lamda=-6`.
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