Question

If $|\vec{a}| = \sqrt{3}$; $|\vec{b}| = 5$; $\vec{b} \cdot \vec{c} = 10$, angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{3}$, $\vec{a}$ is perpendicular to $\vec{b} \times \vec{c}$. Then the value of $|\vec{a} \times (\vec{b} \times \vec{c})|$ is

• A. 20
• B. 30
• C. 60
• D. 40

Hint:

Remember the formulas for dot product and cross product, and how to use the condition of perpendicularity for the angle between vectors. If $\vec{u}$ is perpendicular to $\vec{v}$, then the angle between them is $\frac{\pi}{2}$, and $\sin(\frac{\pi}{2}) = 1$.

Answer 1

The Correct Option is A