Question

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

$3v-2w$

Short answer

The value of $3v-2w$is $13i-21j+10k$

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. Multiply the scalars

Multiply the scalars with vectors,

$$\begin{gathered} 3v-2w=3(3i-5j+2k)-2(-2i+3j-2k) \\ =9i-15j+6k+4i-6j+4k \end{gathered}$$

Step 3. Add the common terms.

$$\begin{gathered} 3v-2w=9i-15j+6k+4i-6j+4k \\ =13i-21j+10k \end{gathered}$$