Show that if a vector in 3 dimensions makes angles a, b, c respectively with the x, y, z axes, then cos^2(a) + cos^2(b) + cos^2(c) = 1.
How do I tackle this question? Thanks.
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.