Question

Given three unit vector $a,b,c$ such that $\mathbf{a}\bot\mathbf{b}$ and $a||c$, then $a \times (b \times c)$ is

• A. a
• B. b
• C. c
• D. 0

Answer 1

Answer: (B)

b

Answer 2

$a \times (b \times c) = (a.c)b - (a.b)c$

$\because\mathbf{a}\bot\mathbf{b},\therefore\mathbf{a}.\mathbf{b} = 0$

$\because$ $\mathbf{a}||\mathbf{c}$, $\therefore\mathbf{a}.\mathbf{c} = 1$ (a, b and c are unit vectors)

$\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = (1)\mathbf{b} - (0)\mathbf{c}$ = b.