Question

The points with position vectors $60i+3j$, $40i-8j$ and $ai-74j$ are collinear, if $a$ is equal to:

• A. $-80$
• B. $-40$
• C. $20$
• D. None of these

Answer 1

Answer: (A)

$-80$

Given points are $60i+3j$ , $40i-8j$ and $ai-74j$

Let the points be $A,B,C$ in order

For it to be collinear , the line $BA$ and $CA$ must be parallel

So we have $BA=-20i-11j$ and $CA=(a-60)i-77j$

Since they are parallel , we get $\frac{a-60}{-20}=\frac{-77}{-11}$

$\Rightarrow a-60=-140$

$\Rightarrow a=-80$

Therefore, option $A$ is correct