# Thread: Prove the cosine rule using vectors

1. ## Prove the cosine rule using vectors

Yr 12 Specialist Mathematics:

Triangle ABC where (these are vectors):
AB = a
BC = b
CA = c
such that a + b = -c

Prove the cosine rule, |c|2= |a|2 + |b|2 -2 |a|.|b| cosB using vectors

So far, I've been able to derive |c|2= |a|2 + |b|2 +2 |a|.|b| cosB, with a positive not a negative. I used dot product rules where c.c = |(-a-b)2|cosB. I'm a bit lost, and could really use some help on how to get the answer!

And this is my first time on these forums XD Could someone please tell me if there are symbols we can use? For pi, square root, things like that?

Much appreciation
-iamapineapple

2. ## Re: Prove the cosine rule using vectors

There's no need for vectors.

3. ## Re: Prove the cosine rule using vectors

Thanks and all, but that's the question I have to answer. "Prove it using vectors"......

4. ## Re: Prove the cosine rule using vectors

Originally Posted by iamapineapple
Yr 12 Specialist Mathematics:
Triangle ABC where (these are vectors):
AB = a
BC = b
CA = c
such that a + b = -c
Prove the cosine rule, |c|2= |a|2 + |b|2 -2 |a|.|b| cosB using vectors
You have several errors there.

From the given, $\cos(B)=\frac{-\vec{a}\cdot\vec{b}}{\|-\vec{a}\|\|\vec{b}\|}$.

$\|\vec{c}\|^2=(-\vec{a}-\vec{b})\cdot(-\vec{a}-\vec{b})=\|(\vec{a}\|^2+\|(\vec{b}\|^2+2\vec{a} \cdot \vec{b}$

,

,

,

,

,

,

,

,

,

,

,

,

,

,

# vector proof of cosine law

Click on a term to search for related topics.