Answer
$13i-21j+10k$
Work Step by Step
Let us consider two vectors $v=pi+qj+rz$ and $w=xi+yj+zk$
The addition of the above vectors can be found by adding the individual components of the vector:
$v+w=(p+x)i+(q+y)j+(r+z)k$
We apply similar reasoning to simplify the given expression:
$3v -2w=3 (3i-5j+2k) -2(-2i+3j-2k) \\
= 9i-15j+6k+4i-6j+4k\\
=13i-21j+10k$
