MHTCET 13 Apr 2026 Shift 2 Paper

Concept:Use the vector triple product identity and compare coefficients of independent vectors.Explanation:The identity is:$\bar{a} \times (\bar{b} \times \bar{c}) = \bar{b}(\bar{a}\cdot\bar{c}) - \bar{c}(\bar{a}\cdot\bar{b})$Given that:$\bar{a} \times (\bar{b} \times \bar{c}) = \frac{\bar{b}}{2}$So we have:$\bar{b}(\bar{a}\cdot\bar{c}) - \bar{c}(\bar{a}\cdot\bar{b}) = \frac{\bar{b}}{2}$Since $\bar{a}, \bar{b}, \bar{c}$ are non-coplanar, $\bar{b}$ and $\bar{c}$ are linearly independent.Hence, the coefficients of $\bar{b}$ and $\bar{c}$ must match on both sides.The right side contains no $\bar{c}$ term, so the coefficient of $\bar{c}$ must be zero:$-(\bar{a}\cdot\bar{b}) = 0$This gives:$\bar{a}\cdot\bar{b} = 0$Therefore, $\bar{a}$ and $\bar{b}$ are perpendicular.The angle between them is $\frac{\pi}{2}$.Answer:The angle is $\frac{\pi}{2}$, which corresponds to option C.