If three points `A ,\ B` and `C` have position vectors ` hat i+x hat j+3 hat k ,\ 3 hat i+4 hat j+7 hat k` and `y hat i-2 hat j-5 hat k` respectively are collinear, them `(x , y)=`

Options

A. a) `(2,-3)`
B. b) `(-2,3)`
C. c) `(-2,-3)`
D. d) `(2,3)`

Answer

c) `(-2,-3)`

Explanation

Given,


`vec(A)=hat i+x hat j+3 hat k`


`vec(B)=3hat i+4 hat j+7 hat k`


`vec(C)=yhat i-2 hat j-5hat k`



`vec(BA)=-2hat i+(x-4 )hat j-4 hat k`


`vec(BC)=(y-3)hat i-6hat j-12 hat k`


Both vectors are collinear:


`vec(BC)=lambdavec(BA)`


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