# Math Help - Components of a Vector

1. ## Components of a Vector

The vector a is in the plane Oxy Where Ox, Oy are the coordinate axes, and makes an angle $30^\circ$ with Ox, as in the above diagram. Find the components of a along Ox, Oy when a equals 10.

$\begin{array}{rcrcrc}
a = 10\\
\cos30 = \frac{A}{10}\\
10\cos30 = A\\
A = 8.66
\end{array}$

$\begin{array}{rcrcrc}
a = 10\\
\sin30 = \frac{opp}{10}\\
10\sin30 = opp\\
opp = 5
\end{array}$

Answer: $|8.66i + 5j|$

Is this right?

2. note that the triangle is a 30-60-90 right triangle ...

hypotenuse = $a$

vertical leg = $\frac{a}{2}$

horizontal leg = $\frac{a}{2} \cdot \sqrt{3}$

3. What does the dot mean? I've decided to do it using trig, as we have other questions similar which don't all have right angle triangles as far as I know. Is there something I have done wrong?

4. Originally Posted by Viral
What does the dot mean? I've decided to do it using trig, as we have other questions similar which don't all have right angle triangles as far as I know. Is there something I have done wrong?
HI

dot means multiply or times .

THere is nothing wrong with your answer , you are correct .

But to avoid confusion , use a different unknown such as x for horizontal and y for vertical . Anyways , it's just my opinion but its advisable for people who tend to mess up things like me .