(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} -4sqrt{2} \ 4sqrt{2} end{pmatrix})
(b) ((r + q) = begin{pmatrix} 0 \ 10 end{pmatrix} + begin{pmatrix} -4sqrt{2} \ 4sqrt{2} end{pmatrix})
= (begin{pmatrix} -4sqrt{2} \ 10 + 4sqrt{2} end{pmatrix})
= (begin{pmatrix} -5.66 \ 15.66 end{pmatrix}).