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:

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For a line making angles with the coordinate axes, use the identity \( \sin^2\alpha + \sin^2\beta + \sin^2\gamma = 1 \).
Updated On: Mar 7, 2025
  • \( 3 \)
  • \( 2 \)
  • \( 1 \)
  • \( \frac{3}{2} \)
  • \( 0 \)
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The Correct Option is C

Solution and Explanation

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, \( \sin^2\alpha + \sin^2\beta - \cos^2\gamma = 1 \).
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