Question

If $\mathbf{a} = 2\mathbf{i} + 3\mathbf{j} - 5\mathbf{k},\mathbf{b} = m\mathbf{i} + n\mathbf{j} + 12\mathbf{k}$ and $\mathbf{a} \times \mathbf{b} = 0,$

then $(m,n) =$

• A. $\left( - \frac{24}{5},\frac{36}{5} \right)$
• B. $\left( \frac{24}{5}, - \frac{36}{5} \right)$
• C. $\left( - \frac{24}{5}, - \frac{36}{5} \right)$
• D. $\left( \frac{24}{5},\frac{36}{5} \right)$

Answer 1

Answer: (C)

$\left( - \frac{24}{5}, - \frac{36}{5} \right)$

Answer 2

\mathbf{i} & \mathbf{j} & \mathbf{k} \\ 2 & 3 & - 5 \\ m & n & 12 \end{matrix} \right|$$ $$= (36 + 5n)\mathbf{i} - (24 + 5m)\mathbf{j} + (2n - 3m)\mathbf{k} = 0$$ $\Rightarrow m = \frac{- 24}{5},n = \frac{- 36}{5}$.