Mathematics

Problem

Two vectors

\mathbf{p}

and

\mathbf{q}

have magnitudes

|\mathbf{p}|=6

and

|\mathbf{q}|=8

. The angle between them is

60^{\circ}

. a. (i) Calculate

\mathbf{p}\cdot\mathbf{q}

. b. (ii) If the magnitude of

\mathbf{q}

is changed to

10

while the angle remains the same, determine the new value of

\mathbf{p}\cdot\mathbf{q}

. c. (iii) Comment, with suitable reasoning, on how changing the magnitude of one vector affects the value of the dot product when the angle is kept fixed.

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