Question

Find direction angles and direction cosines of the following vectors :.
$5\hat{i}+12\hat{j}+84\hat{k}$.

Answer 1

direction ratios of the line are $5,12,84$

direction cosines of the line are

$\frac{5}{\sqrt{{\left(5\right)}^2+{\left(12\right)}^2+{\left(84\right)}^2}},\frac{12}{\sqrt{{\left(5\right)}^2+{\left(12\right)}^2+{\left(84\right)}^2}},\frac{84}{\sqrt{{\left(5\right)}^2+{\left(12\right)}^2+{\left(84\right)}^2}}\frac{5}{85},\frac{12}{85},\frac{84}{85}$