- #1

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## Homework Statement

Pick any numbers that add to

*x*+

*y*+

*z*= 0. Find the angle between your vector

**v**= (

*x, y, z*) and the vector

**w**= (

*z, x, y*). Challenge question: explain why

**v.w**/

**|v||w|**is always -1/2.

## Homework Equations

## The Attempt at a Solution

I chose (1, -2, 1) for the first part, which is straightforward. The second bit has me somewhat flummoxed. Using

*x*,

*y*, and

*z*, I get:

(

*xz + xy + yz*)/(

*x^*2 + y^2 + z^2)

I can see that the numerator will always be less than the denominator because either one or two of the components must be negative. The explanation proper eludes me though, and I feel missing something simple here. Please assist me in understanding this one.