Question

Find direction angles and direction cosines of the given vector.

Answer 1

vector is given $\bf{\hat{j}+\hat{k}}$
we know, The direction cosines of a vector are defined as the coefficients of $\hat{i},\hat{j},\hat{k}$ in the unit vector in the direction of the vector.
So, first we find the unit vector in the direction of the vector.
Let $\bf{\vec{r}=\hat{j}+\hat{k}}$
$|r|=\sqrt{1^2+1^2}=\sqrt{2}$

so, $\hat{r}=\frac{\vec{r}}{|r|}=\frac{\hat{j}+\hat{k}}{\sqrt{2}}$

now, direction cosines of the given vector are 0 , 1/√2 , 1/√2 .

direction angles :-
direction angles can be find by using formula,
if $\vec{r}=a\hat{i}+b\hat{j}+c\hat{k}$
$cos\alpha=\frac{a}{\sqrt{a^2+b^2+c^2}}$

$cos\beta=\frac{b}{\sqrt{a^2+b^2+c^2}}$

$cos\gamma=\frac{c}{\sqrt{a^2+b^2+c^2}}$

so, direction angles of given vectors are : 90° , 45° , 45°

Answer 2

In the attachment I have answered this problem.

The solution is simple and easy to understand.

See the attachment for detailed solution.