Assertion: If three vectors $\vec A$, $\vec B$ and $\vec C$ satisfy $\vec A\cdot\vec B = 0$ and $\vec A\cdot\vec C = 0$, then the vector $\vec A$ is parallel to $\vec B\times\vec C$. Reason: $\vec A\perp\vec B$ and $\vec A\perp\vec C$, hence $\vec A$ is perpendicular to

Question

Assertion: If three vectors $\vec A$, $\vec B$ and $\vec C$ satisfy $\vec A\cdot\vec B = 0$ and $\vec A\cdot\vec C = 0$, then the vector $\vec A$ is parallel to $\vec B\times\vec C$. Reason: $\vec A\perp\vec B$ and $\vec A\perp\vec C$, hence $\vec A$ is perpendicular to the plane formed by $\vec B$ and $\vec C$.

Accepted Answer

Both A and R are true and R is the correct explanation of A.. If $\vec A\cdot\vec B=0$ and $\vec A\cdot\vec C=0$, then $\vec A$ is perpendicular to both $\vec B$ and $\vec C$. Therefore $\vec A$ is normal to the plane containing $\vec B$ and $\vec C$, which is the direction of $\vec B\times\vec C$.

Solution

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