Since we know that the magnitude is 10 and the angle that it does with the x-axis, we can use trigonometry and find out what we want, see the diagram for better explanation.
First of all, let's analyse the angle, 240º is on which part of euclidean plane? the third quadrant, so it means that the x and y value is negative! now we know they're negative me must analyse the triangle to find the values, looking the triangle we did we can see that the y value will be the hypotenuse multiplied by the cosine of the 240º or if we want we can do it with 30º, just adjust the signal after.
Then since we know that h = 10 and we know the cosine and sine we can do
[tex]\Large\displaystyle\text{$\begin{gathered}a = -h\sin 30^\circ\\ \\ a = -\frac{10}{2}\\ \\ a = -5\\ \\\end{gathered}$}[/tex]
And for b,
[tex]\Large\displaystyle\text{$\begin{gathered}b = -h\cos 30^\circ\\ \\b =- \frac{10\sqrt{3}}{2}\\ \\b = -5\sqrt{3}\\ \\\end{gathered}$}[/tex]
Then our vector is
[tex]\Large\displaystyle\text{$\begin{gathered}v = \left(-5, -5\sqrt{3}\right)\end{gathered}$}[/tex]
Hope you liked it
Questions? Ask me in the comments
