Question

Find the direction cosines of the vector joining the points $A(1,2,-3)$ and $B(-1,-2,1)$ directed from $A$ to $B$.

Answer 1

The given points are $A(1,2,-3)$ and $B(-1,-2,1)$.

$\therefore \overrightarrow{AB}=(-1-1)\hat{i}+(-2-2)\hat{j}+\{1-(-3\left)\right\}\hat{k}$

$\therefore \overrightarrow{AB}=-2\hat{i}-4\hat{j}+4\hat{k}$

$\therefore |\overrightarrow{AB}|=\sqrt{(-2{)}^2+(-4{)}^2+4^2}=\sqrt{4+16+16}=\sqrt{36}=6$

Hence, the direction cosines of $\overrightarrow{AB}$ are $(-\frac{2}{6},-\frac{4}{6},\frac{4}{6})=(-\frac{1}{3},-\frac{2}{3},\frac{2}{3})$.