Question

If $\mathbf{a} \times \mathbf{b} = \mathbf{b} \times \mathbf{c} \neq 0$ and $\mathbf{a} + \mathbf{c} \neq 0,$ then

• A. $(\mathbf{a} + \mathbf{c})\bot\mathbf{b}$
• B. $(\mathbf{a} + \mathbf{c})||\mathbf{b}$
• C. $\mathbf{a} + \mathbf{c} = \mathbf{b}$
• D. None of these

Answer 1

Answer: (B)

$(\mathbf{a} + \mathbf{c})||\mathbf{b}$

Answer 2

$\mathbf{a} \times \mathbf{b} = \mathbf{b} \times \mathbf{c} \Rightarrow (\mathbf{a} + \mathbf{c}) \times \mathbf{b} = 0,$ but $\mathbf{a} + \mathbf{c} \neq 0$

$\Rightarrow \mathbf{a} + \mathbf{c}||\mathbf{b}.$