Chapter 9, Problem 33RE

To determine

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

Answer to Problem 33RE

The value of $\Vert v\Vert$ is $\sqrt{5}$ .

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.

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

Therefore, the value of $\Vert v\Vert$ is $\sqrt{5}$ .