Mathematics > vectors > Vectors

Assertion (A): If $|\vec{a} \times \vec{b}|^2 + |\vec{a} \cdot \vec{b}|^2 = 256$ and $|\vec{b}| = 8$, then $|\vec{a}| = 2$. Reason (R): $\sin^2\theta + \cos^2\theta = 1$ and $|\vec{a} \times \vec{b}| = |\vec{a}||\vec{b}|\sin \theta$ and $\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos \theta$.