Answer:
[tex]\vec W = -4\sqrt{3}\,\hat{i}-4\,\hat{j}[/tex], [tex]\vec W = (-4\sqrt{3},-4)[/tex]
Step-by-step explanation:
If [tex]\vec W[/tex] is in standard position, then its direction is counterclockwise with respect to [tex]+x[/tex] semiaxis. A vector is defined by its magnitude and direction, that is:
[tex]\vec W = \|\vec W\| \cdot (\cos \theta\,\hat{i}+\sin \theta \,\hat{j})[/tex] (1)
Where:
[tex]\|\vec W\|[/tex] - Magnitude, no unit.
[tex]\theta[/tex] - Direction, measured in sexagesimal degrees.
If we know that [tex]\|\vec W\| = 8[/tex] and [tex]\theta =210^{\circ}[/tex], then the resulting vector is:
[tex]\vec W = 8\cdot (\cos 210^{\circ}\,\hat{i}+\sin 210^{\circ}\,\hat{j})[/tex]
[tex]\vec W = -4\sqrt{3}\,\hat{i}-4\,\hat{j}[/tex]
Which is also equivalent to:
[tex]\vec W = (-4\sqrt{3},-4)[/tex]
