JEE Advanced 2014 Paper 1 Mathematics Q8

Mathematics

Problem

Let

\vec x,\vec y

and

\vec z

be three vectors each of magnitude

\sqrt2

and the angle between each pair of them is

\frac{\pi}{3}

. If

\vec a

is a nonzero vector perpendicular to

\vec x

and

\vec y\times\vec z

and

\vec b

is a nonzero vector perpendicular to

\vec y

and

\vec z\times\vec x

, then