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## 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!