Show that cos2 alpha cos2 beta cos2 gamma 1 find the

Question

As shown in the figure, the direction cosines represent the cosines of the angles made between the vector and the three coordinate directions.

The direction cosines of a nonzero vector v = A_Xi + A_Yj + A_Zk

cos α = A_X/||v||
cos β = A_Y/||v||
cos γ= A_Z/||v||

where the angles α, β, and γ are the angles shown in the figure.

a. Show that: cos² α + cos² β + cos² γ = 1.

b. Find the direction cosines of the vector v = 2i - 4j + 4k. and approximate the direction angle to the nearest degree.