Question

The points with position vectors if $60i+3j,40i-8j,ai-52j$ are collinear .
Find the value of a.

• A. $a=-20$
• B. $a=-+20$
• C. $a=-40$
• D. $a=+40$

Answer 1

Answer: (C)

$a=-40$

Let $A=60i+3j,B=40i-8j,C=ai-52j$
For these points to be collinear,
slope of line AB = slope of line BC
$\Rightarrow \frac{3+8}{60-40}=\frac{-8+52}{40-a}$
$\Rightarrow \frac{11}{20}=\frac{44}{40-a}\Rightarrow a=-40$