Mathematics

Problem

Two vectors are given by

\mathbf{u}=3\,\hat{i}-\hat{j}+2\,\hat{k}

and

\mathbf{v}=-\hat{i}+4\,\hat{j}+\hat{k}

. Answer the following: a. Write, in vector form only, an expression for the area of the parallelogram having

\mathbf{u}

and

\mathbf{v}

as its adjacent sides. b. Hence calculate the numerical value of this area, correct to two decimal places. c. Determine the area of the triangle formed by the same two vectors.

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