TITLE: "Show" that the direction cosines of a vector satisfies...
QUESTION [5 upvotes]: "Show" that the direction cosines of a vector satisfies
$$\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1$$
I am stumped on these things:

"SHOW" that the direction cosines corresponds to a given vector to satisfy the relation above. ----> How do you "show" this? What does this mean? Does this mean to use the direction cosines of a vector?

I'm sure this is a proof but I don't know what the end result would look like or better, what I am expected to learn from this proof.


I am not looking for a mere answer but really an in-depth explanation of the problem.
Greatly appreciated. :)

REPLY [6 votes]: If $$x^2+y^2+z^2=r^2,$$ then $$\frac{x^2}{r^2}+\frac{y^2}{r^2}+\frac{z^2}{r^2}=1,$$ or $$\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma=1.$$