Chapter 12.R, Problem 4E

Calculate the given quantity if

$\begin{array}{l}a=i+j-2k\\ b=3i-2j+k\\ c=j-5k\end{array}$

(a) $2a+3b$

(b) $\left|b\right|$

(c) $a\cdot b$

(d) $\left(a\times b\right)$

(e) $\left|b\times c\right|$

(f) $a\times \left(b\times c\right)$

(g) $c\times c$

(h) $a\times \left(b\times c\right)$

(i) ${\text{comp}}_{\text{a}}b$

(j) ${\text{proj}}_{\text{a}}b$

(k) The angle between a and b (correct to the nearest degree)