Proving angle sum trig identies w/ vector and scalar products

1. Oct 4, 2012

bossman007

1. The problem statement, all variables and given/known data

I need to prove both of these (in exercise 11)

[PLAIN]http://postimage.org/image/x7shxv11f/ [Broken][/PLAIN]

2. Relevant equations

The dot product

3. The attempt at a solution

Last edited by a moderator: May 6, 2017
2. Oct 4, 2012

clamtrox

What do you mean where did you go wrong? Isn't that what you were asked to prove? You really need to write down some intermediate steps though. It's impossible to follow your "proof" as it is now. Now you just wrote down the starting point and the end result.

3. Oct 4, 2012

vela

Staff Emeritus
Your first mistake is in the very first line: What is $\vec{A}\vec{B}\cos(\theta+\phi)$ supposed to mean? You can't just stick two vectors next to each other like that. $\vec{A}\cdot\vec{B}$ makes sense because it's saying your dotting the two vectors together; similarly, $\vec{A}\times\vec{B}$ makes sense because it's saying you're taking the cross product. $\vec{A}\vec{B}$ doesn't mean anything.

Your second mistake is that you're using the very identity you're trying to prove. So far, you're using the fact that $\vec{A}\cdot\vec{B} = |\vec{A}||\vec{B}|\cos(\theta+\phi)$. You need to find a second way to express the dot product.

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