Chapter 9, Problem 34RE

To determine

To find: The value of $\Vert v\Vert +\Vert w\Vert$ .

Answer to Problem 34RE

The value of $\Vert v\Vert +\Vert w\Vert$ is $7.24$ .

Explanation of Solution

Given information:

The given vectors are

  $v=-2i+j$

  $w=4i-3j$

Calculation:

The magnitude of the vector $v=a_{1}i+b_{1}j$ .

  $\Vert v\Vert =\sqrt{a_1^2+b_1^2}$

Compare the vector $v=-2i+j$ with standard form $v=a_{1}i+b_{1}j$ to obtain the values of $a_1=-2$ and $b_1=1$ .

Calculate the magnitude of the vector.

  $\begin{array}{c}\Vert v\Vert =\sqrt{{\left(-2\right)}^2+{\left(1\right)}^1}\\ =\sqrt{4+1}\\ =\sqrt{5}\end{array}$

The magnitude of the vector $w=a_{1}i+b_{1}j$ .

  $\Vert w\Vert =\sqrt{a_1^2+b_1^2}$

Compare the vector $w=4i-3j$ with standard form $w=a_{1}i+b_{1}j$ to obtain the values of $a_1=4$ and $b_1=-3$ .

Calculate the magnitude of the vector.

  $\begin{array}{c}\Vert w\Vert =\sqrt{{\left(-42\right)}^2+{\left(-3\right)}^2}\\ =\sqrt{16+9}\\ =\sqrt{25}\\ =5\end{array}$

Add the values of two magnitudes.

  $\begin{array}{c}\Vert v\Vert +\Vert w\Vert =\sqrt{5}+5\\ =2.236+5\\ =7.24\end{array}$

Therefore, the value of $\Vert v\Vert +\Vert w\Vert$ is $7.24$ .