JEE Advanced 2021 Paper 1 Mathematics Q19

Mathematics

Problem

Let

\vec{u}

\vec{v}

and

\vec{w}

be vectors in three-dimensional space, where

\vec{u}

and

\vec{v}

are unit vectors which are not perpendicular to each other and

\vec{u}

\vec{w}

= 1,

\vec{v}

\vec{w}

= 1,

\vec{w}

\vec{w}

= 4. If the volume of the parallelopiped, whose adjacent sides are represented by the vectors

\vec{u}

\vec{v}

and

\vec{w}

, is √2, then the value of |3

\vec{u}

+ 5

\vec{v}

| is ___.