If a vector `vec(A)` make angles `alpha , beta ` and `gamma`, respectively , with the `X , Y` and `Z` axes , then `sin^(2) alpha + sin^(2) beta + sin^(2) gamma =`

Options

A. 0
B. 1
C. 2
D. 3

Answer

C

Explanation

If `vec(P)` makes angle `alpha, beta, gamma` respectively with X, Y, Z -axis `cos^(2) alpha+ cos^(2) beta + cos^(2) gamma=1`
`rArr 1- sin^(2) alpha+ 1- sin^(2) beta + 1- sin^(2) gamma=1`
`rArr sin^(2) alpha+ sin^(2) beta+ sin^(2) gamma= 2`