Physics - Vectors Question with Solution | TestHub

Given $\vec{a}\cdot \vec{b}=0$, which implies that $\vec{a}$ is perpendicular to $\vec{b}$.

Given $\vec{a}\cdot \vec{c}=0$, which implies that $\vec{a}$ is perpendicular to $\vec{c}$.

Since $\vec{a}$ is perpendicular to both $\vec{b}$ and $\vec{c}$, it must be perpendicular to the plane containing $\vec{b}$ and $\vec{c}$.

The vector $\vec{b}\times \vec{c}$ is also perpendicular to the plane containing $\vec{b}$ and $\vec{c}$.

Therefore, $\vec{a}$ is parallel to $\vec{b}\times \vec{c}$.

Answer: $\vec{b}\times \vec{c}$