Mathematics

Problem

Two vectors

\vec P

and

\vec Q

have magnitudes

|\vec P| = 7\,\text{units}

and

|\vec Q| = 5\,\text{units}

. a. (i) When the angle between the two vectors is

30^{\circ}

, calculate the magnitude of

\vec P\times\vec Q

. b. (ii) Using the same magnitudes, calculate the magnitude of

\vec P\times\vec Q

when the angle between them is (a)

0^{\circ}

and (b)

90^{\circ}

. c. (iii) Based on your results, briefly comment on the dependence of the cross-product magnitude on the angle between the vectors.