- #1
Dafe
- 145
- 0
Homework Statement
Pick any numbers that add to:
[tex] x + y + z = 0 [/tex]
Find the angle between your vector [tex]\textbf{v} = (x, y, z)[/tex]
and the vecor [tex]\textbf{w} = (z, x, y)[/tex]
Explain why [tex] \textbf{v}\bullet\textbf{w} / ||\textbf{v}||||\textbf{w}|| [/tex] is always [tex] -\frac{1}{2} [/tex]
Homework Equations
Cosine Forumla:
[tex]\frac{\textbf{v}\bullet\textbf{w}}{||\textbf{v}||||\textbf{w}||}=cos\theta[/tex]
The Attempt at a Solution
I pick:
[tex] \textbf{v} = (2, -1, -1) [/tex]
[tex] \textbf{w} = (-1, 2, -1) [/tex]
I insert the integers into the cosine forumla and get [tex] -\frac{1}{2} [/tex]
As for the question why it is always -(1/2), I am not sure where to start.
If you guys could push me in the right direction I would really appreciate it.
Thanks!