If points `A(60 hat i+3 hat j),\ B(40 hat i-8 hat j)a n d\ C(a hat i-52 hat j)` are collinear, then a is equal to `40` b. `-40` c. `20` d. -20

Options

A. 40
B. -40
C. 20
D. -20

Answer

B

Explanation

It is given that points A, B and C are collinear.
` therefore vec (AB) = lambda vec (BC) ` for some scalar ` lambda `
` rArr -20 veci -11 vec j = lambda { (a -40 ) veci -44 vecj}`
`rArr lambda (a -40) = -20, -44 lambda = -11`
`rArr (a-40) = -20 and lambda =(1)/(4)`
`rArr a+40 = -80 rArr a= -40`