Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a} \times(\vec{b} \times \vec{c})=\frac{\sqrt{3}}{2}(\vec{b}+\vec{c})$. If $\vec{b}$ is not parallel to $\vec{c}$, then the angle between $\vec{a}$ and $\vec{b}$ is:

JEE Main · 2016 · 03 Apr 2016 · Offline · Vector Algebra

Let

a, b

and

c

be three unit vectors such that

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

. If

b

is not parallel to

c

, then the angle between

a

and

b

is:

Answer: (C)

Expand the triple product:

a \times (b \times c) = (a \cdot c) b - (a \cdot b) c

, and set it equal to

\frac{3}{2} (b + c)

. Because

b

and

c

are not parallel, their coefficients match separately:

a \cdot c = \frac{3}{2}

and

a \cdot b = - \frac{3}{2}

. For unit vectors

a \cdot b = cos θ

, so

cos θ = - \frac{3}{2}

and the angle between

a

and

b

\frac{5 π}{6}

JEE Main · 2016 · 03 Apr 2016 · Offline · Single correct option