Calculating Sum of 2 Vectors using Laws of Cosine I found this to calculate the sum of 2 vectors with a specific angle $v$:
It's the law of cosine: $$a^2 + b^2 - 2ab\cos(v)$$
Sources are split on this, however ... 
One source says  the one above is the way to go, but others say this one is:
$$a^2 + b^2 +2ab\cos(v) $$
(the same but with + and + instead of + and -)
Could someone please shed a light on this? 
 A: There is an ambiguity here which I think comes from the way
we define the "angle" that is used in the formula.
Consider this visualization of vector addition, copied from
https://en.wikipedia.org/wiki/File:Vector_Addition.svg:

To find the length of $\mathbf a + \mathbf b$, we can apply the
Law of Cosines to one of the two triangles with sides 
$\mathbf a$, $\mathbf b$, and $\mathbf a + \mathbf b$.
Either triangle is OK since they are congruent.
The Law of Cosines tells us that
$$
c^2 = a^2 + b^2 - 2ab \cos \phi
$$
where $a = \|\mathbf a\|$, $b = \|\mathbf b\|$, 
$c = \|\mathbf a + \mathbf b\|$,
and $\phi$ is the angle of the sides $\mathbf a$ and $\mathbf b$ of the triangle.
Depending on which of the two triangles you choose, this is
either the angle where the head of a copy of $\mathbf a$
meets the tail of a copy of $\mathbf b$
or the angle where the head of a copy of $\mathbf b$
meets the tail of a copy of $\mathbf a$.
In other words, to use this formula we should set $\phi$ to one of the
"head-to-tail" angles in the figure.
But when we measure the angle between two vectors, it is more usual
to measure the "tail-to-tail" angle, that is, the angle
in the figure where the tail of a copy of $\mathbf a$
and the tail of a copy of $\mathbf b$ coincide
(which is also the point where the tail of $\mathbf a + \mathbf b$
is drawn in the figure).
Let's write $\alpha$ to denote the "tail-to-tail" angle between the vectors.
Since the copies of $\mathbf a$ and $\mathbf b$
in the figure above form a parallelogram, we know that
$$
\alpha = \pi - \phi
$$
(measured in radians)
and therefore
$$
\cos(\alpha) = -cos(\phi).
$$
Therefore the Law of Cosines actually tells us that
$$
c^2 = a^2 + b^2 + 2ab \cos \alpha.
$$
In other words, whether you have "$+\cos\theta$" or "$-\cos\theta$"
is entirely due to whether you define $\theta$ the way $\phi$
is defined above or the way $\alpha$ is defined above.
The answer  Proof of vector addition formula
comes to this conclusion as well, but the figure that supports that answer 
seems to have been lost.
A: It depends if the angle $v$ is between the two vectors taken ''tail to tail'' or ''head to tail''. This two angles are supplementary. You can  see this answer: Proof of vector addition formula
