# Determining magnitude and direction of vectors

1. Mar 13, 2012

### savva

1. The problem statement, all variables and given/known data
Determine the magnitude and direction θ of F1 so that the resultant force is directed vertically upward and has a magnitude of 800N.

2. Relevant equations
F1=FR-F2-F3

3. The attempt at a solution
I have attached the question with diagram and my attempt at solving the question. I know that by using the equation above, F1=FR-F2-F3, however I am slightly confused as to obtaining the values for these vectors and how to approach doing that.

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• ###### Chp 2 - Q2.21 Problem WORKING.jpg
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2. Mar 13, 2012

### Joffan

Solve for F1x using the horizontal components, solve for F1y using vertical components, then take F1x and F1y to solve for F1 and θ

3. Mar 14, 2012

### savva

Thanks for your help Joffran, I managed to solve the problem with your help, I will add the working I used to solve it tomorrow

4. Mar 16, 2012

### savva

$\Sigma$Fx=0 ----> 400cos30+F1x-(4/5)(600)=0 ----> F1x=133.6N
$\Sigma$Fy=800 ----> 400sin30+F1y+(3/5)(600)=800 ----> F1y=240N

F1= (F1x^2+F2y^2)^.5 = (133.6^2+240^2)^.5=274.7N

tanθ=F1x/F1y=133.6/240

θ=tan^-1(133.6/240)=29.1