Question

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

$||v+w||$

Short answer

The value of $||v+w||$is $\sqrt{5}$

Step-by-step solution

Step 1. Given

The quantities:

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

To find the given values.

Step 2. Combine like terms

Combine like terms

$$\begin{gathered} ||v+w||=||3i-5j+2k+(-2i+3j-2k)|| \\ =||i-2j|| \end{gathered}$$

Step 3. Find the length of the vector

The length of the factor is,

$$\begin{gathered} ||i-2j||=\sqrt{1^2+{(-2)}^2} \\ =\sqrt{1+4} \\ =\sqrt{5} \end{gathered}$$