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

a = - 40

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.