Chapter 10, Problem 21P

Consider vectors:

$\begin{array}{l}\stackrel{\to }{A}=\stackrel{\to }{2i}-\stackrel{\to }{3j}+\stackrel{\to }{ak}\\ \stackrel{\to }{B}=\stackrel{\to }{bi}+\stackrel{\to }{j}-\stackrel{\to }{4k}\\ \stackrel{\to }{C}=\stackrel{\to }{3i}+\stackrel{\to }{cj}+\stackrel{\to }{2k}\end{array}$

Vector $\stackrel{\to }{A}$ is perpendicular to $\stackrel{\to }{B}$ as well as to $\stackrel{\to }{C}$. It is also known that $\stackrel{\to }{B}\cdot \stackrel{\to }{C}=2$. Use any method studied in this chapter to solve for the three unknowns, $a,b,\text{ and }c$.