- #1

- 100

- 16

## Homework Statement

Prove that sum of the cosines squared of the angles between a vector and the x, y, and z axes equals 1. Prove using either geometry or vector algebra.

## Homework Equations

[itex]cos^2(\theta_x)+cos^2(\theta_y)+cos^2(\theta_z)=1[/itex]

## The Attempt at a Solution

I started by trying to pull out the angles with

[itex]\cos^{-1}[/itex]

Getting

[itex]\theta_x+\theta_y+\theta_z=0+2k\pi[/itex]

(Edit: This is no longer valid)

This doesn't make sense to me since I know that the maximum sum of the angles can only be around 180 degrees (I think). So I thought maybe the geometric approach would have something to do with triangles. But I don't know how to show that analytically.

(Edit: Still clueless)

I'm also lost on how to start with the vector algebra. I'm looking over the identities of vectors now but to no avail.

Thoughts?

Last edited: