"Show" that the direction cosines of a vector satisfies... "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:


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*"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?

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*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. :)

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 $$\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma=1.$$
