# Addition of vectors

1. Sep 20, 2011

### asad1111

how to add two vectors knowing only angle between them for example if we have two vectors A and B having angle 40 degrees what will be the resultant sum of two?
also in three phase systems how to find resultant of two voltage of equal magnitude having a phase difference of 120 degrees

2. Sep 20, 2011

### vk6kro

You would need to know the magnitudes of the vectors.

Assuming you do know the magnitudes, you can either draw the vectors on graph paper and measure the resultant, or you can calculate it using the cosine rule:
http://en.wikipedia.org/wiki/Cosine_rule

For example, two 100 volt voltages are 120 degrees apart in phase, calculate the resultant.

C2= 1002 + 1002 - 2 * 100 * 100 * Cos(120)

C = 173 volts

3. Sep 20, 2011

### yungman

You don't have enough info. You need to know the amplitude of the two AND:

1) For 2 space, you need the angle of one of them and know whether the other has angle greater or smaller.

2) For 3 space, you need both $\theta, \phi\;$ of one and at least one angle of the second.

There might be some nifty trick that require less, but not just the angle between them.

4. Sep 20, 2011

### yungman

But that is only relative only, I assume he mean you actually have to find the result vector from addition in absolute position and magnitude.( with specific $\theta , \phi$).

5. Sep 20, 2011

### vk6kro

It is the voltage between phases of a 3 phase system.

What do you mean by "absolute position" with regard to voltages?

6. Sep 20, 2011

### jim hardy

draw them and use the trigonometry you studied in high school ?

you need to do this repeatedly until it becomes as automatic as reciting the alphabet.
Drill , drill, drill !!!

7. Sep 20, 2011

### yungman

He asked the vector question first, so I answer the question straightly as vector addition and not assuming anything even he ask another question about 3 phase. Particular he gave the example of 40 deg between the two vector, that don't trigger anything about 3 phase voltage. For vector addition, you need more info. Actually I have been doing vector calculus and addition of two vector in 3 space in spherical and rectangular coordinates is not that straight forward. Only in rectangular coordinates is straight forward.

Of cause if you look at in context of 3 phase, then it is easy. But is that what he really asking?

Last edited: Sep 20, 2011
8. Sep 20, 2011

### vk6kro

also in three phase systems how to find resultant of two voltage of equal magnitude having a phase difference of 120 degrees

Seems clear enough that we are talking about 3 phase voltages.

9. Sep 21, 2011

### yungman

how to add two vectors knowing only angle between them for example if we have two vectors A and B having angle 40 degrees what will be the resultant sum of two?

This is the first question. And he asked about 40 degree, this don't spell anything about 3 phase voltage. I look at it as two different questions particularly if you read the tittle of the thread. I think you assume the two question is related. Until the op come back and clarify this, I don't think anyone should assume he only talk about 3 phase voltage. Vector happened to be a very important topics in EM and it is not that easy to add two vectors in spherical and cylindrical coordinate that use angle.

10. Sep 21, 2011

### vk6kro

No.
Question 1 was about vectors and we both answered that by saying it needed more information.
Question 2 was about voltages out of phase by 120 degrees. To solve these you could use the rule of cosines and I gave an example of solving a problem like his giving the result for some assumed voltages.

11. Sep 21, 2011

### yungman

You cannot use this to answer the first question. You cannot find the addition of two vector A and B just by specifying only the magnitudes AND the angle between them. You need more information as I explained.

How can you use the cosine law to find C?

I thought $\vec B - \vec A = \vec C\;\Rightarrow\; |\vec C|^2 =|\vec A|^2+|\vec B |^2-2|\vec A||\vec B |\cos \theta$

Cosine law is not to find magnitude of $\vec C =\vec A +\vec B$

$$\vec C = \vec A + \vec B\;\Rightarrow\;|\vec C|=\sqrt{(A_x+B_x)^2+(A_y+B_y)^2+(A_z+B_z)^2}$$

Get more complicate in sph and cyl coordinates.

And you cannot find $\vec C\;$ with only the two amplitude and the angle between them.

I never even touch on the second question as I am not a power engineer.

Last edited: Sep 21, 2011
12. Sep 21, 2011

### sophiecentaur

Where is the problem? You can tell the magnitude of the resultant and its phase, referred to one of the vectors. How could anyone possibly expect to get more info out than that? The orientation of the original vectors in a reference frame is not given.

13. Sep 21, 2011

### sophiecentaur

Where is the problem? You can tell the magnitude of the resultant and its phase, referred to one of the vectors. How could anyone possibly expect to get more info out than that? The orientation of the original vectors in a reference frame is not given.

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