# Math - Geometric Vectors

posted by Anonymous

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.

1. Reiny

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

## Similar Questions

1. ### Math: Calculus - Geometric Vectors

Find the magnitude and the direction of the resultant of each of the following systems of forces using geometric vectors. a) Forces of 3 N and 8 N acting at an angle of 60 degrees to each other. Please help me with this question. I …
2. ### Math: Calculus - Vectors

Two forces of 90 N act on an object. The forces make an angle of 48 degrees to each other. Calculate the resultant force and the force that must be applied to the object to create equilibrium. My work, using geometric vectors: | r …
3. ### physics

Find the magnitude and direction of a)the resultant b)the equilibrant of two forces 10N acting in the direction N030'E and 15N acting in the eastern direction if boths forces act at a point. Please solve nd give the details especially …
4. ### physics

a body is under of 2 forces 7n and 10n find the resultant of 2 forces if (a)the forces are parallel and act in thesame direction (b)the forces are parallel and act in opposite direction(c)the two forces are inclined and act at an angle …
5. ### physics

a body is under of 2 forces 7n and 10n find the resultant of 2 forces if (a)the forces are parallel and act in thesame direction (b)the forces are parallel and act in opposite direction(c)the two forces are inclined and act at an angle …
6. ### Physics

Two forces 10 N acting in the direction N 30 east and 15 N acting in the eastern direction, if both forces act at a point, find the magnitude and direction of (a) the resultant force (b) the equilibriant force.