Chapter 6.4, Problem 19E

To determine

To Find:- Magnitude using dot product.

Answer to Problem 19E

Magnitude of given vector is 32.01.

Explanation of Solution

Given information:

  $u=20i+25j$

Formula used: -

  $\begin{array}{l}u.u=\left|\left|u\right|\right|\left|\left|u\right|\right|\cos \theta \\ u.u=a.a+b.b\end{array}$

  $\begin{array}{l}u.u=\left|\left|u\right|\right|\left|\left|u\right|\right|\cos \theta \\ \cos \theta =0\\ u.u={\left|\left|u\right|\right|}^2\\ \sqrt{u.u}=\left|\left|u\right|\right|\end{array}$

Putting values

  $\begin{array}{l}\Vert u\Vert =\sqrt{\left(20\right)\left(20\right)+\left(25\right)\left(25\right)}\\ =\sqrt{400+625}\\ =\sqrt{1025}\\ \Vert u\Vert =32.01\end{array}$