Greeting all,

I have a question regarding the addition of two vector magnitudes. Generally I've read that we can use this formula:

$\sqrt{A^2 + B^2}$

But what is the different between that formula above and the one like this?

$\sqrt{A^2 + B^2 + 2ABcos\theta}$

I'm sorry if my question is too simple for this sub-forum section, I just seem to be confused with this very part.

Thank You

2. @Lites, you must be a lot more specific in the wording of your question.
Really neither of those is correct without further qualifications.

For example if you have a vector in $\mathbb{R}^2$ say $\vec{U}=$ then its length is $\left\|\vec{U} \right\|=\sqrt{a^2+b^2}$.
That is close to your first example.

3. Originally Posted by Lites
Greeting all,

I have a question regarding the addition of two vector magnitudes. Generally I've read that we can use this formula:

$\sqrt{A^2 + B^2}$
First, what do you mean by "addition of two vector magnitudes". If you mean "find the magnitude of the sum of two vectors, having magnitudes A and B", then what you give is true only if the two vectors are perpendicular- it is from the Pythagorean theorem which applies to right triangles.

But what is the different between that formula above and the one like this?

$\sqrt{A^2 + B^2 + 2ABcos\theta}$
This is the magnitude of the sum of two vectors having magnitudes A and B which form angle $\theta$, not necessarily perpendicular. Notice that if $\theta= \pi/2$, then $cos(\theta)= 0$ so you get the same thing as before. It is from the cosine law that generalizes the Pythagorean theorem to general triangles.

I'm sorry if my question is too simple for this sub-forum section, I just seem to be confused with this very part.

Thank You

4. Originally Posted by Plato
@Lites, you must be a lot more specific in the wording of your question.
Really neither of those is correct without further qualifications.

For example if you have a vector in $\mathbb{R}^2$ say $\vec{U}=$ then its length is $\left\|\vec{U} \right\|=\sqrt{a^2+b^2}$.
That is close to your first example.

This is the magnitude of the sum of two vectors having magnitudes A and B which form angle $\theta$, not necessarily perpendicular. Notice that if $\theta= \pi/2$, then $cos(\theta)= 0$ so you get the same thing as before. It is from the cosine law that generalizes the Pythagorean theorem to general triangles.