Question

Which expression gives the magnitude of \[\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}\]?

Options

• \[|\vec{r}|=x^2+y^2+z^2\]

• \[|\vec{r}|=\sqrt{x+y+z}\]

• \[|\vec{r}|=x+y+z\]

• \[|\vec{r}|=\sqrt{x^2+y^2+z^2}\]

Answer 1

The magnitude is found by taking the square root of the sum of the squares of the three components. Thus \[|\vec{r}|=\sqrt{x^2+y^2+z^2}\].