Question

If $\mathbf { x } \cdot \mathbf { a } = 0 , \mathbf { x } \cdot \mathbf { b } = 0$ and $\mathbf { x } \cdot \mathbf { c } = 0$ for some non-zero vector x, then the true statement is

• A.
• B. $\left[ \begin{array} { l l l } \mathbf { a } & \mathbf { b } & \mathbf { c } \end{array} \right] \neq 0$
• C. $\left[ \begin{array} { l l l } \mathbf { a } & \mathbf { b } & \mathbf { c } \end{array} \right] = 1$
• D. None of these

Answer 1

Answer: (A)

Answer 2

Since is a non-zero vector, the given conditions will be satisfied, if either (i) at least one of the vectors $\mathbf { a } , \mathbf { b } , \mathbf { c }$ is zero or (ii) is perpendicular to all the vectors $\mathbf { a } , \mathbf { b } , \mathbf { c }$ In case (ii), $\mathbf { a } , \mathbf { b } , \mathbf { c }$ are coplanar and so