If points $A(60\hat i+ 3\hat j), B(40\hat i-8\hat j)$ and $C (a\hat i-52\hat j)$ are collinear, then a is equal to

-40

It is given that points A, B and C are collinear.

$∴\vec{AB} = 2\vec{BC}$ for some scalar $λ$

$⇒-20\hat i-11\hat j =λ \{(a-40)\hat i -44\hat j\}$

$⇒λ (a-40)=-20, -44λ=-11$

$⇒λ (a-40)=-20$ and $λ=\frac{1}{4}$

$⇒a-40=-80⇒a=-40$