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 $\sqrt{38}-\sqrt{17}$

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. Find the length of the vector.

Find the length of the vector separately.

$$\begin{gathered} ||v||=||3i-5j+2k|| \\ =\sqrt{3^2+{(-5)}^2+{\left(2\right)}^2} \\ =\sqrt{9+25+4} \\ =\sqrt{38} \end{gathered}$$

$$\begin{gathered} ||w||=||-2i+3j-2k|| \\ =\sqrt{{(-2)}^2+3^2+{(-2)}^2} \\ =\sqrt{17} \end{gathered}$$

Step 3. Find the required quantity.

The required value is,

$||v||-||w||=\sqrt{38}-\sqrt{17}$