If a, b, c are non-coplanar unit vectors such that a × (b × c) = dfrac(b + c)√(2), then the angle between a and b is

If a, b, c are non-coplanar unit vectors such that a × (b ×… — JEE Main 1995 Mathematics PYQ

1995

\vec{a}, \vec{b}, \vec{c}

are non-coplanar unit vectors such that

\vec{a} \times (\vec{b} \times \vec{c}) = \dfrac{(\vec{b} + \vec{c})}{\sqrt{2}}

, then the angle between

\vec{a}

and

\vec{b}

A.
$\dfrac{3\pi}{4}$
B.
$\dfrac{\pi}{4}$
C.
$\dfrac{\pi}{2}$
D.
$\pi$

Show answer and solution

Correct option: A

Solution

Using the BAC-CAB rule: a×(b×c) = (a·c)b - (a·b)c = (b+c)/√2.

So (a·c) = 1/√2 and -(a·b) = 1/√2, giving a·b = -1/√2.

Since all are unit vectors, a·b = |a||b|cosθ = cosθ = -1/√2, so θ = 3π/4.

[1995]

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JEE Main 1995 Mathematics question on Vector Algebra