The points with position vectors `60hati+3hatj,40hati-8hatj, 40hati-8hatj,ahati-52hatj` are collinear iff (A) `a=-40` (B) `a=40` (C) `a=20` (D) none of these

Options

A. `a= -40 `
B. `a=40`
C. `a=20`
D. none of these

Answer

A

Explanation

Three points `A(veca) , B (vecb), C(vecc)` are collinear if `vec(AB)"||"vec(AC)`
`vec(AB) = -20 hati -11hatj, vec(AC) = (a- 60)hati -55 hatj`
`rArr vec(AB) "||" vec(AC) rArr (a- 60)/(-20) = (-55)/(-11) or a = -40`