Hello, classicstrings,

let s be the length of the vector v.

Then v can be expressed by its coordinates:

v = (s*cos(a), s*cos(b), s*cos(c)= s * (cos(a), cos(b), cos(c))

Now calculate the length of v:

|v| = s = sqrt(sē*cosē(a) + sē*cosē(b) + sē*cosē(c)) = s * sqrt(cosē(a) + cosē(b) + cosē(c))

Divide both sides of this equation by s and you'll get:

1 = sqrt(cosē(a) + cosē(b) + cosē(c))

Squaring both sides of the last equation will give the desired result.

EB