jee-main 2015 Q82

jee-main · India · 10apr Vectors: Cross Product & Distances

Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be three non-zero vectors such that no two of them are collinear and $(\vec{a} \times \vec{b}) \times \vec{c} = \frac{1}{3}|\vec{b}||\vec{c}|\vec{a}$. If $\theta$ is the angle between vectors $\vec{b}$ and $\vec{c}$, then a value of $\sin\theta$ is:
(1) $\frac{2\sqrt{2}}{3}$
(2) $-\frac{\sqrt{2}}{3}$
(3) $\frac{2}{3}$
(4) $-\frac{2\sqrt{3}}{3}$

Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be three non-zero vectors such that no two of them are collinear and $(\vec{a} \times \vec{b}) \times \vec{c} = \frac{1}{3}|\vec{b}||\vec{c}|\vec{a}$. If $\theta$ is the angle between vectors $\vec{b}$ and $\vec{c}$, then a value of $\sin\theta$ is:\\
(1) $\frac{2\sqrt{2}}{3}$\\
(2) $-\frac{\sqrt{2}}{3}$\\
(3) $\frac{2}{3}$\\
(4) $-\frac{2\sqrt{3}}{3}$

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