Question

Select correct option from the given options.

Answer 1

vector is given $\bf{\vec{x}=-2\hat{i}+\hat{j}-2\hat{k}}$

firs of all , find magnitude of given vector
e.g., $\bf{|x|=\sqrt{(-2)^2+1^2+(-2)^2}}$
$\bf{|x|=\sqrt{4+1+4}=3}$

now, unit vector is written by of any vector r ,
= $\boxed{\bf{\hat{r}=\frac{\vec{r}}{|r|}}}$

now, unit vector of given vector, x
= $\hat{x}=\frac{\vec{x}}{|x|}=\frac{-2\hat{i}+\hat{j}-2\hat{k}}{3}$

$\hat{x}=\frac{-2}{3}\hat{i}+\frac{1}{3}\hat{j}+\frac{-2}{3}\hat{k}$

hence, unit vector , $\hat{x}=(-2/3,1/3,-2/3)$

hence, option (b) is correct.

Answer 2

In the attachment I have answered this problem.

The solution is simple and easy to understand.

Option b is correct

See the attachment for detailed solution.