The points with position vectors $60\hat i+3\hat j$, $40\hat i-8\hat j$ and $a\hat i-52\hat j$ are collinear if
Answer & explanation
Correct answer: option 1
The points are collinear
$λ(60\hat i+3\hat j) + μ(40\hat i-8\hat j) + ν(a\hat i-52\hat j) = 0$ with $ λ +μ + ν = 0$
$60λ + 40μ + νa = 0$,
$3λ – 8μ – 52ν = 0$,
$ λ +μ + ν = 0$
For non-zero set $(λ,μ,ν), \begin{vmatrix}60&40&a\\3&-8&-52\\1&1&1\end{vmatrix}= 0 ⇒ a = – 40$
Hence (A) is the correct answer.