JEE Advanced 2014 Paper 1 Mathematics Q20

Mathematics

Problem

Let

\vec a,\vec b

and

\vec c

be three non-coplanar unit vectors such that the angle between every pair of them is

\frac{\pi}{3}

. If

\vec a\times\vec b+\vec b\times\vec c=p\vec a+q\vec b+r\vec c

, where

p,q

and

r

are scalars, then the value of

\dfrac{p^2+2q^2+r^2}{q^2}