Question

The points with position vectors $10i+3j,12j$ and $ai+11j$ are collinear then a equals.

Answer 1

$\begin{array}{c}\overrightarrow{A}\left(10\hat{i}+3\hat{j}\right)\overrightarrow{B}\left(12\right)\hat{j}\overrightarrow{C}\left(a\hat{i}+11\hat{j}\right)\\ \overrightarrow{AB}=-10\hat{i}+9\hat{j}\\ \overrightarrow{AC}=\left(a-10\right)\hat{i}+8\hat{j}\\ \overrightarrow{AB}and\overrightarrow{AC}arecollinear.\\ \Rightarrow \frac{-10}{a-10}=\frac{9}{8}\\ \frac{10}{10-a}=\frac{9}{8}\\ 80=90-9a\\ 9a=10\\ \therefore a=\frac{10}{9}\end{array}$