JEE Advanced 2013 Paper 1 Mathematics Q10

Mathematics

Problem

Let

\overrightarrow{PR}=3\hat{i}+\hat{j}-2\hat{k}

and

\overrightarrow{SQ}=\hat{i}-3\hat{j}-4\hat{k}

determine diagonals of a parallelogram

PQRS

and

\overrightarrow{PT}=\hat{i}+2\hat{j}+3\hat{k}

be another vector. Then the volume of the parallelepiped determined by the vectors

\overrightarrow{PT}

\overrightarrow{PQ}

and

\overrightarrow{PS}