## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$13i-21j+10k$
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: $3v -2w=3 (3i-5j+2k) -2(-2i+3j-2k) \\ = 9i-15j+6k+4i-6j+4k\\ =13i-21j+10k$