Question

A line makes angles \( \alpha, \beta, \gamma \) with \( x, y \), and \( z \)-axes respectively. Then the value of \( \sin^2\alpha + \sin^2\beta - \cos^2\gamma \) is:

• A. \( 3 \)
• B. \( 2 \)
• C. \( 1 \)
• D. \( \frac{3}{2} \)
• E. \( 0 \)

Hint:

For a line making angles with the coordinate axes, use the identity \( \sin^2\alpha + \sin^2\beta + \sin^2\gamma = 1 \).

Answer 1

The Correct Option is C

Using the property of a line making angles with the axes, we know that: \[ \sin^2\alpha + \sin^2\beta + \sin^2\gamma = 1 \] Thus, \( \sin^2\alpha + \sin^2\beta - \cos^2\gamma = 1 \).