Question

Find the length of each of the vectors$\stackrel{\mathbf{\rightharpoonup }}{\mathbf{v}}$In exercises 1 through 3.

1. $\stackrel{\mathbf{\rightharpoonup }}{\mathbf{v}}\mathbf{=}\left[\begin{array}{c}7\\ 11\end{array}\right]$

Short answer

The length of the vector is about 13.04.

Step-by-step solution

Consider the definition below

The length(or magnitude or norm) of a vector$\stackrel{\mathbf{\rightharpoonup }}{\mathbf{v}}\mathbf{}\mathbf{in}\mathbf{}{\mathit{R}}^{\mathbf{n}}\mathbf{}\mathbf{is}\mathbf{}\mathbf{\left|}\left|\stackrel{\rightharpoonup }{v}\right|\mathbf{\right|}\mathbf{=}\sqrt{\stackrel{\mathbf{\rightharpoonup }}{\mathbf{v}}\mathbf{}\mathbf{.}\stackrel{\mathbf{\rightharpoonup }}{\mathbf{v}}\mathbf{}}$.

According to the definition

By using the above definition, the length of the vector will be.

$$\begin{gathered} \left||\stackrel{\rightharpoonup }{\mathrm{v}}|\right|=\sqrt{\stackrel{\rightharpoonup }{\mathrm{v}}.\stackrel{\rightharpoonup }{\mathrm{v}}} \\ =\sqrt{\left[711\right]\left[\begin{array}{c}7\\ 11\end{array}\right]} \\ =\sqrt{7.7+11.11} \\ =\sqrt{49+121} \\ =\sqrt{170} \\ =13.04 \end{gathered}$$

Hence, the value of the vector is about 13 .04 .