Question

Find the direction ratios and the direction cosines of the vector $\overrightarrow{a}=(5\hat{i}-3\hat{j}+4\hat{k}).$.

Answer 1

Given the vector is.........

$\overline{a}=\left(5\hat{i}-3\hat{j}+4\hat{k}\right)$

Then,

The Direction ratio is...........(5,-3,4)

a=5,b=-3,c=4

And,

The magnitude of $\overline{a}$ =$\sqrt{{\left(5\right)}^2+{\left(-3\right)}^2+{\left(4\right)}^2}$

= $\sqrt{25+9+16}$

= $\sqrt{25+25}$

= $\sqrt{50}$

= $5\sqrt{2}$

Now,

The Direction cosines of the vector is= $\left[\frac{5}{5\sqrt{2}},\frac{-3}{5\sqrt{2}},\frac{4}{5\sqrt{2}}\right]$