If `alpha , beta, gamma` be angles which the vector `vec(r)=lambda vec(i)+2vec(j)-vec(k)` makes with the coordinate axes, then what is the value of `sin^(2)alpha+sin^(2) beta+sin^(2)gamma`?

Options

A. `2`
B. `1`
C. `lambda^(2)+1`
D. `1-lambda^(2)`

Answer

A

Explanation

We know that for any line that makes `alpha, beta and gamma ` angle with 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`