Question

If the points with position vectors $60i+3j,40i-8j$and $ai-52j$are collinear, then $a$ is equal to?

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

Answer 1

The correct option is A

$-40$

Step 1: Apply condition for collinearity,

Let, $X$, $Y$ and $Z$ denotes the position vectors $60i+3j,40i-8j$ and $ai-52j$ respectively.

Now, if $X$, $Y$ and $Z$ are collinear, then

Slope of line $XY$ = Slope of line $YZ$

$\frac{(3+8)}{(60-40)}=\frac{(-8+52)}{(40-a)}$

Step 2: Solve the above equation for $a$

$\Rightarrow$ $\frac{11}{20}=\frac{44}{(40-a)}$

$\Rightarrow$$11(40-a)=\left(44\right)\left(20\right)$

$\Rightarrow$ $(40-a)=80$

$\Rightarrow$ $a=-40$

Hence, option A is the correct option.