The three vectors and taken two at a time form three planes

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

The three vectors

\hat{i} + \hat{j}, \hat{j} + \hat{k}

and

\hat{k} + \hat{i}

taken two at a time form three planes. If

V

be the volume of the tetrahedron having adjacent sides as the three unit vectors drawn perpendicular to those three planes, then find the value of

9\sqrt{3}V