Chapter 3, Problem 13Q

Which of the following are correct (meaningful) vector expressions? What is wrong with any incorrect expression?

$\begin{array}{l}\begin{array}{cc}\begin{array}{l}\text{(a) }\stackrel{\to }{A}\cdot (\stackrel{\to }{B}\cdot \stackrel{\to }{C})\\ \text{(b) }\stackrel{\to }{A}\times (\stackrel{\to }{B}\cdot \stackrel{\to }{C})\\ \text{(c) }\stackrel{\to }{A}\cdot (\stackrel{\to }{B}\times \stackrel{\to }{C})\\ \text{(d) }\stackrel{\to }{A}\times (\stackrel{\to }{B}\times \stackrel{\to }{C})\\ \text{(e) }\stackrel{\to }{A}+(\stackrel{\to }{B}\cdot \stackrel{\to }{C})\end{array}& \end{array}\\ \text{(f) }\stackrel{\to }{A}+(\stackrel{\to }{B}\times \stackrel{\to }{C})\\ \text{(g) }5+\stackrel{\to }{A}\\ \text{(h) }5+(\stackrel{\to }{B}\cdot \stackrel{\to }{C})\\ \text{(i) }5+(\stackrel{\to }{B}\times \stackrel{\to }{C})\\ \text{(j) }(\stackrel{\to }{A}\cdot \stackrel{\to }{B})+(\stackrel{\to }{B}\times \stackrel{\to }{C})\end{array}$