# Components of a Vector

• Sep 22nd 2009, 08:51 AM
Viral
Components of a Vector

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

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

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

Answer: $\displaystyle |8.66i + 5j|$

Is this right?
• Sep 22nd 2009, 01:53 PM
skeeter
note that the triangle is a 30-60-90 right triangle ...

hypotenuse = $\displaystyle a$

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

horizontal leg = $\displaystyle \frac{a}{2} \cdot \sqrt{3}$
• Sep 22nd 2009, 11:07 PM
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?
• Sep 23rd 2009, 12:21 AM