Chapter 9.6, Problem 44AYU

In Problems 39-44, find each quantity if $v=3i-5j+2k$ and $w=-2i+3j-2k$.

$\Vert v\Vert +\Vert w\Vert$

To determine

To find: $\left|\right|v\left|\right| + \left|\right|w\left|\right|$

Answer to Problem 44AYU

Solution:

$\sqrt{38} + \sqrt{17}$

Explanation of Solution

Given:

$\begin{array}{l}v = 3i - 5j + 2k\\ w = -2i + 3j - 2k\end{array}$

Calculation:

$\begin{array}{l}\left|\right|v\left|\right| = \sqrt{3^2 + {(-5)}^2 + 2^2}\\ \left|\right|v\left|\right| = \sqrt{9 + 25 + 4}\\ \left|\right|v\left|\right| = \sqrt{38}\\ \left|\right|w\left|\right| = \sqrt{{(-2)}^2 + 3^2 + {(-2)}^2}\\ \left|\right|w\left|\right| = \sqrt{4 + 9 + 4}\\ \left|\right|w\left|\right| = \sqrt{17}\\ \left|\right|v\left|\right| + \left|\right|w\left|\right| = \sqrt{38} + \sqrt{17}\end{array}$