Chapter 9, Problem 41RE

To determine

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

Answer to Problem 41RE

The value of $\Vert v-w\Vert$ is $\sqrt{38}$ .

Explanation of Solution

Given information:

The first vector is

  $v=3i+j-2k$

The second vector is

  $w=-3i+2j-k$

Calculation:

The length of the vector is calculated as

  $\begin{array}{c}\Vert v\Vert =\Vert ai+bj+ck\Vert \\ =\sqrt{a^2+b^2+c^2}\end{array}$

Calculate the value of $\Vert v-w\Vert$ .

  $\begin{array}{c}\Vert v-w\Vert =\Vert \left(3i+j-2k\right)-\left(-3i+2j-k\right)\Vert \\ =\Vert \left(3i+j-2k\right)+3i-2j+k\Vert \\ =\Vert 6i-j-k\Vert \end{array}$

  $\begin{array}{c}\Vert v-w\Vert =\sqrt{6^2+{\left(-1\right)}^2+{\left(-1\right)}^2}\\ =\sqrt{36+1+1}\\ =\sqrt{38}\end{array}$

Therefore, the value of $\Vert v-w\Vert$ is $\sqrt{38}$ .