Express (14N, 240°) as a column vector.
A. \(\begin{pmatrix} -7 \\ -7\sqrt{3} \end{pmatrix}\)
B. \(\begin{pmatrix} 7\sqrt{3} \\ 7\sqrt{3} \end{pmatrix}\)
C. \(\begin{pmatrix} -7\sqrt{3} \\ -7 \end{pmatrix}\)
D. \(\begin{pmatrix} 7 \\ -7\sqrt{3} \end{pmatrix}\)
Correct Answer: A
Explanation
\(F = \begin{pmatrix} F_{x} \\ F_{y} \end{pmatrix} = \begin{pmatrix} F\cos \theta \\ F\sin \theta \end{pmatrix}\)
\((14N, 240°) = \begin{pmatrix} 14\cos 240 \\ 14\sin 240 \end{pmatrix}\)
= \(\begin{pmatrix} 14 \times -0.5 \\ 14 \times \frac{-\sqrt{3}}{2} \end{pmatrix}\)
= \(\begin{pmatrix} -7 \\ -7\sqrt{3} \end{pmatrix}\)
