<P> It follows that by squaring each equation and adding the results </P> <Dl> <Dd> cos 2 ⁡ a + cos 2 ⁡ b + cos 2 ⁡ c = 1 . (\ displaystyle \ cos ^ (2) a+ \ cos ^ (2) b+ \ cos ^ (2) c = 1 .) </Dd> </Dl> <Dd> cos 2 ⁡ a + cos 2 ⁡ b + cos 2 ⁡ c = 1 . (\ displaystyle \ cos ^ (2) a+ \ cos ^ (2) b+ \ cos ^ (2) c = 1 .) </Dd> <P> Here α, β and γ are the direction cosines and the Cartesian coordinates of the unit vector v / v, and a, b and c are the direction angles of the vector v . </P>

Sum of the squares of direction sines is