Mathematics

Problem

Vectors

\mathbf{p}

and

\mathbf{q}

have magnitudes

|\mathbf{p}|=10

units and

|\mathbf{q}|=15

units. The angle between them, when they are placed with a common tail, is

60^\circ

. a. (i) Calculate the magnitude of the resultant vector

\mathbf{R}=\mathbf{p}+\mathbf{q}

. b. (ii) Find the angle between

\mathbf{R}

and

\mathbf{p}

. c. (iii) Suppose instead that

\mathbf{q}

is placed first and

\mathbf{p}

second while keeping the same

60^\circ

between them. Show numerically that the magnitude of the resultant remains the same although the angle it makes with

\mathbf{q}

changes correspondingly.