Question

Find a unit vector that has the same direction as the given vector. −3i + 2j − k

Answer 1

Answer:

Explanation:

Suppose vector is given by

$\vec{r}=-3\hat{i}+2\hat{j}-\hat{k}$

unit vector in direction of $\vec{r}$ is given by

$\hat{r}=\frac{\vec{r}}{|r|}$

where |r| is absolute value of $\vec{r}$

$|r|=\sqrt{(-3)^2+(2)^2+(-1)^2}=\sqrt{14}$

$\hat{r}=\frac{-3\hat{i}+2\hat{j}-\hat{k}}{\sqrt{14}}$