Practicing Success
Vectors $\vec a$ and $\vec b$ are inclined at an angle θ = 60°. If $|\vec a|=1,|\vec b|=2$, then $[(\vec a + 3\vec b) × (3\vec a -\vec b)]^2$ is equal to |
225 275 325 300 |
300 |
We have, $[(\vec a + 3\vec b) × (3\vec a -\vec b)]^2$ $=[10 (\vec b×\vec a)]^2$ $=100|\vec b×\vec a|^2$ $=100\left\{|\vec a|^2|\vec b|^2-(\vec a.\vec b)^2\right\}$ $=100(4-2\cos 60°)=300$ $[∵\vec a.\vec b=2\cos 60°=1$ |