Let a, b, and c be three non-coplanar unit vectors such that the angle between every pair of them is 3 . If a b + b c = p a + q b + r c, where p, q and r are scalars, then the value of p^2 + 2q^2 + r^2 q^2 is

JEE Advanced 2014 Mathematics question

Let , , and be three non-coplanar unit vectors such that the angle between every pair of them is . If , where p, q and r are scalars, then the value of is

Answer: 4

Solution

Each dot product between different vectors is ; let . Dot both sides with : . With : . With : \frac\frac$

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Question ID VK-026303