Chapter 10, Problem 22P

Consider the following vectors:

$\begin{array}{l}\stackrel{\to }{A}=\stackrel{\to }{ai}+\stackrel{\to }{bj}+\stackrel{\to }{ck}\\ \stackrel{\to }{B}=-\stackrel{\to }{2i}+\stackrel{\to }{j}-\stackrel{\to }{4k}\\ \stackrel{\to }{C}=\stackrel{\to }{i}+\stackrel{\to }{3j}+\stackrel{\to }{2k}\end{array}$

Where $\stackrel{\to }{A}$ is an unknown vector. If

$\left(\stackrel{\to }{A}\times \stackrel{\to }{B}\right)+\left(\stackrel{\to }{A}\times \stackrel{\to }{C}\right)=\left(5a+6\right)\stackrel{\to }{i}+\left(3b-2\right)\stackrel{\to }{j}+\left(-4c+1\right)\stackrel{\to }{k}$

use any method learned in this chapter to solve for the three unknowns, a, b, andc.