Question

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

Answer 1

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

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

$\widehat{AB}=\frac{-1}{3}\hat{i}-\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}$

Hence, direction cosines of the required vector are $\frac{-1}{3},\frac{-2}{3},\frac{2}{3}$.