If x, a, b and c are non-zero vectors such that a.x=0, b.x=0 and c.x=0, then [abc] is

Question

If $\mathbf{x}, \mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are non-zero vectors such that $\mathbf{a} \cdot \mathbf{x}=0, \mathbf{b} \cdot \mathbf{x}=0$ and $\mathbf{c} \cdot \mathbf{x}=0$, then $[\mathbf{a b c}]$ is

(a) 0

(b) |a||b||c|

(c) $\frac{1}{3}|\mathbf{a}||\mathbf{b}||\mathbf{c}|$

(d) None of these

Answer 1

$\mathbf{x}$ is perpendicular to $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ it means $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are coplanar, so $[\mathbf{a} \mathbf{b} \mathbf{c}]=\mathbf{0}$

So, The correct option of this question will be (A).