Question

Given r= -i+2j+2k, find the magnitude of r

Answer 1

we know that if

$\overrightarrow{r}= x\hat{i}+y\hat{j}+z\hat{k}$ then magnitude of $\overrightarrow{r}$ is given by

$$|\overrightarrow{r}|=\sqrt{x^2+y^2+z^2}$$

here $\overrightarrow{r} = -\hat{i} + 2\hat{j} + 2\hat{k}$

$\therefore |\overrightarrow{r}|=\sqrt{(-1)^2+2^2+2^2}$

$or,|\overrightarrow{r}| = \sqrt{1+4+4}$

$or,|\overrightarrow{r}|=\sqrt{9}$

$or,|\overrightarrow{r}|=3.$

Answer: magnitude of $\overrightarrow{r} \,\text{is}\,3.$