Question

A line makes angles $\alpha ,\beta ,\gamma$ with the coordinate axes respectively, then $si{n}^2\alpha +si{n}^2\beta +si{n}^2\gamma$ is equal to

• A. 1
• B. 3
• C. 2
• D. 4

Answer 1

Answer: (C)

2

Direction cosines relation -

$co{s}^2\alpha +co{s}^2\beta +co{s}^2\gamma =1$

$1-si{n}^2\alpha +1-si{n}^2\beta +1-si{n}^2\gamma =1$

$\Rightarrow si{n}^2\alpha +si{n}^2\beta +si{n}^2\gamma =3-1=2$

$\therefore si{n}^2\alpha +si{n}^2\beta +si{n}^2\gamma =2$