Question

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

Solution

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To find magnitude\textbf{magnitude} or length\textbf{length} of the vector vv, you can apply next Formula\textbf{Formula}:

v=v12+v22\boxed{\quad ||\text{v}||=\sqrt{{\text{v}_1}^2+{\text{v}_2}^2}\quad}

where v1v_1 and v2v_2 are components of vv.

v=24,7v1=24,v2=7\text{v}=\left\langle -24,7 \right\rangle \Rightarrow\quad \text{v}_1=-24, \text{v}_2=7

Therefore,

v=(24)2+72=576+49=625=25\begin{align*} ||\text{v}||&=\sqrt{(-24)^2+7^2}\\ &=\sqrt{576+49}\\ &=\sqrt{625}\\ &=25 \end{align*}

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