Question

The points, whose position vectors are $60i+3j$, $40i-8j$ and $ai-52j$ collinear, if

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

Answer 1

Answer: (B)

$(40i-8j)-(60i+3j)=\lambda [(ai-52j)-(40i-8j)]$
For some scalar $\lambda$,
$-20=\lambda (a-40)$ and $-11=-44\lambda$
$\Rightarrow a-40=\frac{-20}{\lambda }$ and $\lambda =\frac{1}{4}$
$\Rightarrow a=40-\frac{20}{1}\times 4=-40$