Question

$\mathbf{r} \times \mathbf{a} = \mathbf{b} \times \mathbf{a};\mathbf{r} \times \mathbf{b} = \mathbf{a} \times \mathbf{b};\mathbf{a} \neq 0;\mathbf{b} \neq 0;\mathbf{a} \neq \lambda\mathbf{b},$ a is not

perpendicular to b, then $\mathbf{r} =$

• A. $\mathbf{a} - \mathbf{b}$
• B. $\mathbf{a} + \mathbf{b}$
• C. $\mathbf{a} \times \mathbf{b} + \mathbf{a}$
• D. $\mathbf{a} \times \mathbf{b} + \mathbf{b}$

Answer 1

Answer: (B)

$\mathbf{a} + \mathbf{b}$

Answer 2

$\mathbf{r} \times \mathbf{a} - \mathbf{b} \times \mathbf{a} = 0$ and $\mathbf{r} \times \mathbf{b} + \mathbf{b} \times \mathbf{a} = 0$

Adding, we get $\mathbf{r} \times (\mathbf{a} + \mathbf{b}) = 0$

But as we are given $\mathbf{a} \neq \lambda\mathbf{b},$ therefore $\mathbf{r} = \mathbf{a} + \mathbf{b}.$