Given the vectors and

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

Problem

Given the vectors

\mathbf{a}=2\mathbf{i}-\mathbf{j}+3\mathbf{k}

and

\mathbf{b}=-\mathbf{i}+4\mathbf{j}+2\mathbf{k}

, answer the following: (i) Obtain a non–zero vector

\mathbf{v}

that is perpendicular to both

\mathbf{a}

and

\mathbf{b}

. (ii) Verify analytically that the vector obtained in part (i) is perpendicular to each of

\mathbf{a}

and

\mathbf{b}

. (iii) From the vector found in part (i), write the two possible unit vectors that are perpendicular to both

\mathbf{a}

and

\mathbf{b}

. Explain, with reasons, how the choice of sign distinguishes between the two possible directions.