Question

Find the length and the direction of the resultant of each of the following systems of forces:

a) forces of 3 N and 8 N acting at an angle of 60° to each other


I'm completely lost. I don't know how to solve this question using geometric vectors. Please walk me through the question.

Answer 1

draw two lines from the same point so they form a 60º angle to each other, make one line 8 units long and the other 6.

This is half of a parallelogram,so finish the parallelogram by having opposite sides 8 and 6 respectively and the opposite angle as 60º.

Draw the diagonal between the two 60º vertices.
This line is your resultant, let's call its length x units

now by the Cosine Law
x^2 = 6^2 + 8^2 - 2(6)(8)cos 120º
I get x = 12.1655

Now let the angle between the 8 unit line and the resultant be α

then sinα/6 = sin 120/12.1655

for that I got α = 25.28º

So the resultant is 12.1655 units long and makes an angle of 25.28º with the 8 unit vector