Question

The points with position vectors $60\hat{i}+3\hat{j}$, $40\hat{i}-8\hat{j}$, $a\hat{i}-52\hat{j}$ are collinear if

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

Answer 1

The correct option is A $a=-40$

Three points $A\left(\overrightarrow{a}\right),B\left(\overrightarrow{b}\right),C\left(\overrightarrow{c}\right)$ are collinear if $\overrightarrow{AB}||\overrightarrow{AC}$

$\overrightarrow{AB}=-20\hat{i}-11\hat{j}$

$\overrightarrow{AC}=(a-60)\hat{i}-55\hat{j}$
$\Rightarrow \overrightarrow{AB}||\overrightarrow{AC}$

$\Rightarrow \frac{a-60}{-20}$$=\frac{-55}{-11}$

$\Rightarrow a=-40$