Question

What the direction cosines of the vector $-2\hat{i}+\hat{j}-5\hat{k}$.

Answer 1

Direction cosines of vector $-\hat{i}+\hat{j}-\hat{k}$ are
$\left[\begin{array}{c}\frac{-2}{\sqrt{(-2{)}^2+1^2+(-5{)}^2}},\frac{1}{\sqrt{(-2{)}^2+1^2+(-5{)}^2}},\frac{-5}{\sqrt{(-2{)}^2+1^2+(-5{)}^2}}\\ \frac{-2}{\sqrt{30}},\frac{1}{\sqrt{30}},\frac{-5}{\sqrt{30}}\end{array}\right]$
Note : if I, m , n are direction cosine of $a\hat{i}+b\hat{j}+c\hat{k}$ then $l=\frac{a}{\sqrt{a^2+b^2+c^2}},m=\frac{b}{\sqrt{a^2+b^2+c^2}},n=\frac{c}{\sqrt{a^2+b^2+c^2}}$