# Vector which has same angle with x,y,z axes

## Homework Statement

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How do i find a vector that has same angle with the three coordinate axes (x,y,z)?

## The Attempt at a Solution

I immediately thought [1,1,1] would be it but it's not. I'm trying to find a plane whose normal vector forms the same angle with the three coordinate axes.

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Bacle2
Why doesn't v=(1,1,1) work?

Let e,i,j stand for (1,0,0) ,(0,1,0) and (0,0,1) respectively.

Using a.b=|a||b|cost,

Then v.e=v.i=v.j =1 ; |e|=|i|=|j|=1 .Then

v.e/|v||e|= v.i/|v|.|i|= v.j/|v||j|=cost

Or did you have a different notion of angle in mind?

Last edited:
hmm...it does work....

HallsofIvy
If $\alpha$, $\beta$, and $\gamma$ are three angles, the unit vector that makes angle $\alpha$ with the x-axis, angle $\beta$ with the y-axis and $\gamma$ with the z-axis is $cos(\alpha)\vec{i}+ cos(\beta)\vec{j}+ cos(\gamma)\vec{k}$. If all angles are the same, those three cosines are the same so any vector of the form (x, x, x), and in particular (1, 1, 1) will make equal angles with the three coordinate axes.
perhaps you are looking for the unit vector. The length of (x, x, x) is $\sqrt{x^2+ x^2+ x^2}= x\sqrt{3}$ and we want that equal to 1: we want $x= 1/\sqrt{3}= \sqrt{3}/3$. The unit vector that makes equal angles with the coordinate axes is $(\sqrt{3}/3, \sqrt{3}/3, \sqrt{3}/3)$.