# How to find resultant for 3 given vectors

1. Oct 2, 2005

### idon'tgetit

We were given this problem over the weekend, but our teacher never explained how to do it and we have a quiz on vectors tomorrow and it may be on it. I tried, but couldn't get it...
- Find the resultant of the three vectors A=(-4.0 m) on x-axis + (2.0 m) on y-axis, B= (6.0 m) on x-axis + (3.5 m) on y-axis, and C= (-5.5 m) on y-axis.

I drew it out and drew the vectors tip to tail, but I have no idea a resultant can be made from three vectors. I was thinking maybe the component method, but that would be 6 triangles and it didn't seem right. Please help!

2. Oct 2, 2005

### mlowery

I am a senior in physics, so I'm not exactly an expert. But I have already completed that chapter. Simply add all of the Y's to find the y-component of Vr ($$V_ry$$). Next, add all of the X's to find the X component of Vr ($$V_rx$$). Then:
$$V_r = \sqrt{V_ry^2 + V_rx^2}$$

Correct me please if I am mistaken (physics is giving me trouble).

3. Oct 2, 2005

### HallsofIvy

Staff Emeritus
You find the resultant of three vectors the same way you find the resultant of two- you add them! Yes, you can draw them "tail to tip" and treat it as a geometry problem- although the geometry is a little complicated.

Probably the simplest way is to do what mlowrey said: convert each into x and y components, add the x-components, add the y-components.

If you are not comfortable with components and have only used "triangles" to add two vectors then you can do that also. Start with two of the vectors, draw them "tail to tip" and use the cosine law and sine law to find the resultant. Now take that resultant vector do exactly the same to add it to the third vector.