JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q85

← JEE Main 2016 · 3 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 85 of 90

Let $\vec a$ , $\vec b$ and $\vec c$ be three unit vectors such that $\vec a\times\left(\vec b\times\vec c\right)=\dfrac{\sqrt3}2\left(\vec b+\vec c\right)$ . If $\vec b$ is not parallel to $\vec c$ , then the angle between $\vec a$ and $\vec b$ is :

\dfrac{3\pi}4

\dfrac\pi2

\dfrac{2\pi}3

\dfrac{5\pi}6

Answer and worked solution

Official answer: D

$(\vec a\cdot\vec c)\vec b-(\vec a\cdot\vec b)\vec c=\frac{\sqrt3}2\vec b+\frac{\sqrt3}2\vec c$ . Since $\vec b$ and $\vec c$ are independent, $\vec a\cdot\vec b=-\frac{\sqrt3}2$ , so the angle is $\frac{5\pi}6$ .

Topics:Scalar and vector triple products

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 85