Question

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

$2v+3w$

Short answer

The value of $2v+3w$ is $-j-2k$

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,

$$\begin{gathered} 2v+3w=2(3i-5j+2k)+3(-2i+3j-2k) \\ =6i-10j+4k-6i+9j-6k \end{gathered}$$

Step 3. Add the common terms.

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