Question

Find the direction ratios and the direction cosines of the vector joining the points $A(2,1,-2)$ and $B(3,5,-4).$

Answer 1

$A(2,1,-2)$ and $B(3,5,-4)$

Direction ratios will be $(\overrightarrow{b}-\overrightarrow{a})$ in vector form.

$\therefore$directions $=(3-2)\hat{i}+(5-1)\hat{j}+(-4+2)\hat{k}$

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

$\therefore$ direction cosines$=\frac{\overrightarrow{r}}{\left|\overrightarrow{r}\right|}=\frac{\hat{i}+4\hat{j}-2\hat{k}}{\sqrt{2}}$

direction cosines$=(\frac{1}{\sqrt{2}},\frac{4}{\sqrt{2}},\frac{-2}{\sqrt{2}})$