Question

Write the vector v in the form ai + bj, given its magnitude $||v||$and the angle $\alpha$it makes with the positive x-axis.

$$\begin{gathered} ||v||=3 \\ \alpha ={240}^{\mathrm{o}} \end{gathered}$$

Short answer

The vector v can be written as $-\frac{3}{2}\mathbf{i}-\frac{3\sqrt{3}}{2}\mathbf{j}$.

Step-by-step solution

Step 1. Given information 

We have been given:

$$\begin{gathered} ||v||=3 \\ \alpha ={240}^{\mathrm{o}} \end{gathered}$$

We have to write it in ai+bj form.

Step 2. Substitute the values in v=v(cosαi+sinαj).

$\begin{array}{r}\mathbf{v}=3\left(\cos \left({240}^{\circ }\right)\mathbf{i}+\sin \left({240}^{\circ }\right)\mathbf{j}\right)\\ \mathbf{v}=3\cdot \left(-\frac{1}{2}\mathbf{i}-\frac{\sqrt{3}}{2}\mathbf{j}\right)\\ \mathbf{v}=-\frac{3}{2}\mathbf{i}-\frac{3\sqrt{3}}{2}\mathbf{j}\end{array}$