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,B,C are collinear, if $\overrightarrow{AB}=-20\hat{i}-11\hat{j}$ and $\overrightarrow{AC}=(a-60)\hat{i}-55\hat{j}$, are parallel.
$\overrightarrow{AB}||\overrightarrow{AC}\Rightarrow \frac{a-60}{-20}=\frac{-55}{-11}\Rightarrow a=-40$