1. ## Triple vector problem

Three forces in a plane act on an object. The forces are 7 N, 11 N, and 15 N. The angle between the 7 N and 11 N forces is 105degrees, between the 11 N and 15 N forces is 147degrees, and between the 15 N and 7 N forces is 108degrees.

a) Are the vectors in equilibrium?

b) If not, find the magnitude and the direction of the resultant force.

I can do problems with two vectors just fine, but I'm not sure how to solve with three vectors.

2. ## Re: Triple vector problem

What happens if you ignore the thrid for a moment and calculate the resultant of the other two?

3. ## Re: Triple vector problem

project each vector on coordinate system (x,y for instance or x,y,z for 3 dimensional)
and calculate. if the sum equals zero then vectors in equilibrium.
else you'll have new vector coordinates.

4. ## Re: Triple vector problem

I can't really make any ordered pairs out of these vectors because none of them are in standard position.

If I calculated the resultant of just two vectors, let's say the 7 N and 11 N vectors, I would get:

sqrt{(11)^2 + (15)^2 - 2(11)(15)cos33degrees} = 8.32 N

5. ## Re: Triple vector problem

Originally Posted by explodingtoenails
I can't really make any ordered pairs out of these vectors because none of them are in standard position.
then make a sketch and place them in standard position ...

6. ## Re: Triple vector problem

I only know their y-values though, so I still couldn't turn them into points.

7. ## Re: Triple vector problem

Originally Posted by explodingtoenails
I only know their y-values though, so I still couldn't turn them into points.
x-components for the three ...

$\displaystyle 7$

$\displaystyle 11\cos(105)$

$\displaystyle 15\cos(-108)$

resultant of the x-components ...

$\displaystyle R_x = 7 + 11\cos(105) + 15\cos(-108)$

y-components for the three ...

$\displaystyle 0$

$\displaystyle 11\sin(105)$

$\displaystyle 15\sin(-108)$

resultant of the y-components ...

$\displaystyle R_y = 0 + 11\sin(105) + 15\sin(-108)$

8. ## Re: Triple vector problem

Why did you use 105 and not 147 to measure the x value of the 11 N vector?

9. ## Re: Triple vector problem

Originally Posted by explodingtoenails
Why did you use 105 and not 147 to measure the x value of the 11 N vector?
because my calculator uses the positive x-axis as the reference direction

10. ## Re: Triple vector problem

So to get the x-value of a line segment you multiply its length by the cosine of the reference angle?

11. ## Re: Triple vector problem

Originally Posted by explodingtoenails
So to get the x-value of a line segment you multiply its length by the cosine of the reference angle?
correction ...

to get the x-component of a vector in standard position

12. ## Re: Triple vector problem

So the coordinate pairs for the three vectors would be:

for the 7 N = (7,0)

for the 11 N = (-2.847009496,11)

for the 15 N = (4.635254916,-15)

13. ## Re: Triple vector problem

Originally Posted by explodingtoenails
So the coordinate pairs for the three vectors would be:

for the 7 N = (7,0)

for the 11 N = (-2.847009496,11)

for the 15 N = (4.635254916,-15)
these are incorrect ... see post #7 again

14. ## Re: Triple vector problem

Originally Posted by skeeter
these are incorrect ... see post #7 again
I took a break from this problem and I still can't solve it. Can you please explain what I'm doing wrong?

15. ## Re: Triple vector problem

Originally Posted by explodingtoenails
I took a break from this problem and I still can't solve it. Can you please explain what I'm doing wrong?
I have no idea ... you haven't shown any work.

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