Let a, b and c be three unit vectors such that a × (b × c) = frac√(3)2(b + c). If b is not parallel to c, then the angle between a and b is

Let a, b and c be three unit vectors such that a × (b × c)… — JEE Main 2016 Mathematics PYQ

JEE Main 2016

Let

\hat{a}

\hat{b}

and

\hat{c}

be three unit vectors such that

\hat{a} \times (\hat{b} \times \hat{c}) = \frac{\sqrt{3}}{2}(\hat{b} + \hat{c})

. If

\hat{b}

is not parallel to

\hat{c}

, then the angle between

\hat{a}

and

\hat{b}

A.
$\frac{3\pi}{4}$
B.
$\frac{\pi}{2}$
C.
$\frac{2\pi}{3}$
D.
$\frac{5\pi}{6}$

Show answer and solution

Correct option: D

Solution

Using the BAC-CAB rule: â × (b̂ × ĉ) = (â·ĉ)b̂ - (â·b̂)ĉ = (√3/2)(b̂ + ĉ).

Since b̂ and ĉ are not parallel, we can equate coefficients:
â·ĉ = √3/2 and â·b̂ = -√3/2.

Since all are unit vectors, â·b̂ = cos(angle between â and b̂) = -√3/2, which gives the angle = 5π/6.

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