# Finding the components of a vector along two other vectors

Using only the diagram above (Not using the questions in the diagram), i am asked to find the components of F2 along F1 and F3.

I am having trouble with this question. I can easily resolve any of the vectors into their x and y components but I am not 100% certain how to resolve it along the other vectors. Am I correct in saying that to resolve F2 along F1 we draw a line down directly from the head of F2 to F1 and then take 750*Cos(45) to get the component parallel to F1. What should I do to resolve F2 along F3?

The answer is given as 1240N and 884N. Any hints on how to get to those answers would be much appreciated. Perhaps I am not understanding what is meant by resolving a vector along another vector?

• To be clear, you need to something different from the questions posed in the displayed questions, right? Because 2-36 and 2-37 aren't asking for that. – Wasabi Aug 2 '16 at 23:16
• This link has a way, but when I tried it I did not get the answers you posted in the question: math.stackexchange.com/questions/286391/… – willpower2727 Aug 3 '16 at 12:41

From the geometry $a_1=45 {}^{\circ}$ and $a_2=\tan ^{-1}\left(\frac{3}{4}\right)$ are known and $c_1$ and $c_2$ need to be determined.
$$750 \cos \left(a_1\right)-c_2 \cos \left(a_2\right)=c_1$$
$$c_2 \sin \left(a_2\right)+750 \sin \left(a_1\right)=0$$
This will give $$c_1=875 \sqrt{2}=1237.44$$ and $$c_2=-625 \sqrt{2}=-883.883$$