Electricity: electric field in a point Between Two Charges

[Epoch]

Homework Statement

I've seen many books writing the cosine rule like this:
a^2 = b^2 + c^2 - 2bc cos A

My electricity textbook for an electric field in a point between two charges says this:
E resultant = root[E1^2 + E2^2 + 2*E1*E2*cos(angle between E1 and E2)]

In the first equation it is -2 and in my textbook it is +2.
Why is this?
Because if I use the -2 in my exercises it is wrong and the +2 is right.

Homework Equations

The Attempt at a Solution

I don't really have an attempt since it is more a theoretical question.
I understand how to use it, but I don't understand the +2 and -2.

 

[Doc Al]

I've seen many books writing the cosine rule like this:
a^2 = b^2 + c^2 - 2bc cos A

Note that this applies to a triangle. A is the angle between sides b & c of the triangle.

My electricity textbook for an electric field in a point between two charges says this:
E resultant = root[E1^2 + E2^2 + 2*E1*E2*cos(angle between E1 and E2)]

If you draw a diagram of the vector sum of E1 and E2, you'll see that the angle that applies to the cosine rule is not the angle between those vectors. Instead it is $A = \pi - \theta$. Note that $\cos(\pi -\theta) = -\cos\theta$.

 

[Epoch]

Note that this applies to a triangle. A is the angle between sides b & c of the triangle.If you draw a diagram of the vector sum of E1 and E2, you'll see that the angle that applies to the cosine rule is not the angle between those vectors. Instead it is $A = \pi - \theta$. Note that $\cos(\pi -\theta) = -\cos\theta$.

So is it still called the cosine rule in electricity or does this formula have a specific name?

 

[Doc Al]

So is it still called the cosine rule in electricity or does this formula have a specific name?

No reason to give that formula a special name. You're just adding vectors using the cosine rule. (There are other ways to add vectors. This is just one.)

 

[Epoch]

No reason to give that formula a special name. You're just adding vectors using the cosine rule. (There are other ways to add vectors. This is just one.)

Thanks.