## Related questions with answers

Question

Find the magnitude of v. $\mathbf{v}=\langle-24,7\rangle$

Solution

VerifiedStep 1

1 of 2To find $\textbf{magnitude}$ or $\textbf{length}$ of the vector $v$, you can apply next $\textbf{Formula}$:

$\boxed{\quad ||\text{v}||=\sqrt{{\text{v}_1}^2+{\text{v}_2}^2}\quad}$

where $v_1$ and $v_2$ are components of $v$.

$\text{v}=\left\langle -24,7 \right\rangle \Rightarrow\quad \text{v}_1=-24, \text{v}_2=7$

Therefore,

$\begin{align*} ||\text{v}||&=\sqrt{(-24)^2+7^2}\\ &=\sqrt{576+49}\\ &=\sqrt{625}\\ &=25 \end{align*}$

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