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If a vector vec(A) make angles alpha , b...

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 =`

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
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`
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