Question

If the vectors $i + 3j - 2k$, $2i - j + 4k$ and $3i + 2j + xk$ are coplanar, then the value of x is

• A. – 2
• B. 2
• C. 1
• D. 3

Answer 1

Answer: (B)

2

Answer 2

Vectors $\mathbf{i} + 3\mathbf{j} - 2\mathbf{k};2\mathbf{i} - \mathbf{j} + 4\mathbf{k}$ and $3\mathbf{i} + 2\mathbf{j} + x\mathbf{k}$.

We know that as the vectors are coplanar, therefore

$\left| \begin{aligned} & 13 - 2 \\ & 2 - 14 \\ & 32x \end{aligned} \right| = 0$⇒ $1( - x - 8) - 3(2x - 12) - 2(4 + 3) = 0$

⇒ $- x - 8 - 6x + 36 - 14 = 0$ ⇒ $7x = 14$ ⇒ $x = 2$.