Question

Vector W is in standard position, and makes an angle of 210 degrees with the positive x-axis, it's magnitude is 8. Write W in component form (a,b), and in linear combination form, ai+bj.

Answer 1

Answer:

$\vec W = -4\sqrt{3}\,\hat{i}-4\,\hat{j}$, $\vec W = (-4\sqrt{3},-4)$

Step-by-step explanation:

If $\vec W$ is in standard position, then its direction is counterclockwise with respect to $+x$ semiaxis. A vector is defined by its magnitude and direction, that is:

$\vec W = \|\vec W\| \cdot (\cos \theta\,\hat{i}+\sin \theta \,\hat{j})$ (1)

Where:

$\|\vec W\|$ - Magnitude, no unit.

$\theta$ - Direction, measured in sexagesimal degrees.

If we know that $\|\vec W\| = 8$ and $\theta =210^{\circ}$, then the resulting vector is:

$\vec W = 8\cdot (\cos 210^{\circ}\,\hat{i}+\sin 210^{\circ}\,\hat{j})$

$\vec W = -4\sqrt{3}\,\hat{i}-4\,\hat{j}$

Which is also equivalent to:

$\vec W = (-4\sqrt{3},-4)$