If `alpha, beta and lambda ` are the angles which the vector `vec(OP)` (O being the origin ) makes with positive direction of the coordinate axes, then which of the following are correct?
1. ` cos^(2) alpha + cos^(2) beta = sin^(2) lambda`
2. `sin^(2) alpha + sin^(2) beta=cos^(2)lambda`
3. `sin^(2) alpha + sin^(2)beta + sin^(2)lambda=2`
Select the correct answer using the code given below.

Options

A. 1 and 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1,2 and 3

Answer

C

Explanation

We know, `cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`
`rArr cos^(2)alpha+cos^(2)beta=1-cos^(2)gamma = sin^(2)gamma`
`:.` Statement 1 is correct.
Now, `cos^(2)alpha+cos^(2)beta+cos^()gamma=1`
`rArr 1-son^(2)alpha + 1-sin^(2)beta + 1 - sin^(2)gamma=1`
`rArr 3-(sin^(2)alpha+sin^(2)beta+sin^(2)gamma)=1rArr sin^(2) alpha + sin^(2) beta + sin^(2)gamma=2`.
`:.` Statement 3 is correct.