Mathematics

Problem

Let

\vec a = 2\mathbf i-3\mathbf j+\mathbf k

and

\vec b = \mathbf i+4\mathbf j-2\mathbf k

. a. (i) Find a vector of magnitude

6

that is perpendicular to both

\vec a

and

\vec b

. b. (ii) Calculate the area of the parallelogram having

\vec a

and

\vec b

as its adjacent sides. c. (iii) Determine the area of the triangle whose two sides are represented by

\vec a

and

\vec b