1. ## Cartesian Vectors

Andrew and David kick a football at the same time. Andrew kicks it with a force 155N and David kicks it with a force 210N. Angle between the two forces is 30 degrees. Calculate the magnitude and direction of the resultant force.

Magnitude = Sqrt (155^2 + 210^2 - 2(155)(210)cos30 )
= 108.38N

Direction: Use sine law

I don't understand why the answer at the back of the book used cos 150.
If I were to draw the diagram, would the 2 vectors appear in quadrant 2?
Are they assuming that one of the vectors is parallel to the x axis? (like this):

I was assuming that the vectors were at an angle to the x axis, so that's why I used cos 30...

2. To add two vectors you "connect them head to tail". Your picture should have, say, the 150 N vector beginning at the tip of the 210 N vector. When you do that, the angle between them will be 180- 30= 150 degrees. You are calculating the difference of the two vectors, not their sum.