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 $\sqrt{105}$

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.

$$\begin{gathered} ||v-w||=||3i-5j+2k-(-2i+3j-2k)|| \\ =||3i-5j+2k+2i-3j+2k|| \\ =||5i-8j+4k|| \end{gathered}$$

Step 3. Find the length of the vector

The length of the factor is,

$$\begin{gathered} ||5i-8j+6k||=\sqrt{5^2+{(-8)}^2+4^2} \\ =\sqrt{25+64+16} \\ =\sqrt{105} \\ =\sqrt{105} \end{gathered}$$