(a) Write the following as column vectors: \(r = (10N, 090°) ; q = (8N, 135°)\).
(b) Use your answer in (a) to find \((r + q)\).
Explanation
(a) \(r = (10N, 090°) = \begin{pmatrix} 10 \cos 90° \\ 10 \sin 90° \end{pmatrix}\)
= \(\begin{pmatrix} 0 \\ 10 \end{pmatrix}\)
\(q = (8N, 135°) = \begin{pmatrix} 8 \cos 135° \\ 8 \sin 135° \end{pmatrix}\)
= \(\begin{pmatrix} -8 \cos 45° \\ 8 \sin 45° \end{pmatrix}\)
= \(\begin{pmatrix} -4\sqrt{2} \\ 4\sqrt{2} \end{pmatrix}\)
(b) \((r + q) = \begin{pmatrix} 0 \\ 10 \end{pmatrix} + \begin{pmatrix} -4\sqrt{2} \\ 4\sqrt{2} \end{pmatrix}\)
= \(\begin{pmatrix} -4\sqrt{2} \\ 10 + 4\sqrt{2} \end{pmatrix}\)
= \(\begin{pmatrix} -5.66 \\ 15.66 \end{pmatrix}\).
