JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q85

← JEE Main 2015 · 4 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 85 of 90

Let $\vec a$ , $\vec b$ and $\vec c$ be three non-zero vectors such that no two of them are collinear and $(\vec a\times\vec b)\times\vec c=\dfrac13|\vec b||\vec c|\vec a$ . If θ is the angle between vectors $\vec b$ and $\vec c$ , then a value of $\sin\theta$ is :

\dfrac{2\sqrt2}3

\dfrac{-\sqrt2}3

\dfrac23

\dfrac{-2\sqrt3}3

Answer and worked solution

Official answer: A

$(\vec a\times\vec b)\times\vec c=(\vec a\cdot\vec c)\vec b-(\vec b\cdot\vec c)\vec a$ . Since $\vec a$ and $\vec b$ are not collinear, compare coefficients: $\vec a\cdot\vec c=0$ and $-\vec b\cdot\vec c=\frac13|\vec b||\vec c|$ .

So $\cos\theta=-\frac13$ and $\sin\theta=\dfrac{2\sqrt2}3$ .

Topics:Scalar and vector triple products

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JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 85