Question

If the vectors $4i + 11j + mk,7i + 2j + 6k$ and $i + 5j + 4k$ are coplanar, then m is

• A. 38
• B. 0
• C. 10
• D. – 10

Answer 1

Answer: (C)

10

Answer 2

$\because$ The vectors $4\mathbf{i} + 11\mathbf{j} + m\mathbf{k},7\mathbf{i} + 2\mathbf{j} + 6\mathbf{k}$ and $\mathbf{i} + 5\mathbf{j} + 4\mathbf{k}$ are coplanar.

4 & 11 & m \\ 7 & 2 & 6 \\ 1 & 5 & 4 \end{matrix} \right| = 0$$ $$\Rightarrow 4(8 - 30) - 11(28 - 6) + m(35 - 2) = 0$$ $\Rightarrow - 88 - 11 \times 22 + 33m = 0 \Rightarrow - 8 - 22 + 3m = 0$ $\Rightarrow 3m = 30$ $\Rightarrow m = 10.$