(a) Two vectors are given by and . (i) Set up the determinant whose expansion gives .…

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

Problem

(a) Two vectors are given by

\vec{a}=2\,\hat{i}-3\,\hat{j}+\hat{k}

and

\vec{b}=\hat{i}+4\,\hat{j}-2\,\hat{k}

. (i) Set up the

3\times3

determinant whose expansion gives

\vec{a}\times\vec{b}

. (ii) Expand the determinant to find

\vec{a}\times\vec{b}

. (iii) Hence calculate

|\,\vec{a}\times\vec{b}\,|

. (iv) Using your answer to part (iii), determine the area of the parallelogram whose adjacent sides are represented by

\vec{a}

and

\vec{b}