To express (14N, 240°) as a column vector, we need to convert the given magnitude and direction into horizontal and vertical components.
We can start by drawing a diagram with a vector starting at the origin and pointing in the direction of 240°. We can then use trigonometry to find the horizontal and vertical components.
The horizontal component (x-coordinate) is given by the magnitude (14N) multiplied by the cosine of the angle (240°):
$$\text{Horizontal component} = 14\cos(240°) = 14\left(-\frac{1}{2}\right) = -7$$
The vertical component (y-coordinate) is given by the magnitude multiplied by the sine of the angle:
$$\text{Vertical component} = 14\sin(240°) = 14\left(-\frac{\sqrt{3}}{2}\right) = -7\sqrt{3}$$
Therefore, the column vector representing (14N, 240°) is:
$$\begin{pmatrix} -7 \\ -7\sqrt{3} \end{pmatrix}$$
So the answer is option A: \(\begin{pmatrix} -7 \\ -7\sqrt{3} \end{pmatrix}\).