Question

Three vectors $\vec{A}$, $\vec{B}$ and $\vec{C}$ are such that $\vec{A}\cdot\vec{B} = \vec{A}\cdot\vec{C} = 0$, then $\vec{A}$ is parallel to
$\left[\cos 90^\circ = 0\right]$

• A. $\vec{B}\cdot\vec{C}$
• B. $\vec{B} \times \vec{C}$
• C. $\vec{C}$
• D. $\vec{B}$

Hint:

A vector perpendicular to two vectors is always along their cross product.

Answer 1

The Correct Option is B

Step 1: Interpret dot product conditions.
Given $\vec{A}\cdot\vec{B} = 0$ and $\vec{A}\cdot\vec{C} = 0$, hence $\vec{A}$ is perpendicular to both $\vec{B}$ and $\vec{C}$.

Step 2: Direction perpendicular to both vectors.
The vector perpendicular to both $\vec{B}$ and $\vec{C}$ is given by their cross product $\vec{B} \times \vec{C}$.

Step 3: Conclusion.
Therefore, $\vec{A}$ is parallel to $\vec{B} \times \vec{C}$.