List of top Mathematics Questions on Scalar and Vector Product asked in CBSE Class XII

If for two unit vectors \( \vec{a} \) and \( \vec{b} \), \( |\vec{a} + 2\vec{b}| = |2\vec{a} - \vec{b}| \), then find the angle between \( \vec{a} \) and \( \vec{b} \).

For any two vectors \( \vec{a} \) and \( \vec{b} \), which of the following statements is always true ?

If \( (\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) = 198 \) and \( |\vec{a}| = 10 |\vec{b}| \), then :

Assertion (A): $|\vec{a} \times \vec{b}|^2 + (\vec{a} \cdot \vec{b})^2 = |\vec{a}|^2|\vec{b}|^2$.
Reason (R): $|\vec{a} \times \vec{b}| = (\vec{a} \cdot \vec{b})\tan\theta$, where $\theta$ is the angle between vectors $\vec{a}$ and $\vec{b}$ ($\theta \neq \frac{\pi}{2}$).