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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:
3
`cos^(2)alpha + cos^(2) beta + cos^(2) gamma = 1 `
`1-sin^(2)alpha + 1-sin^(2)beta+1-sin^(2)gamma =1 `
`3- (sin^(2) alpha + sin^(2) beta + sin^(2) gamma)=1`
`sin^(2) alpha + sin^(2) beta + sin^(2) gamma = 3-1 =2`
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