Question

If a line makes \(\alpha, \beta, \gamma\) with the positive direction of x, y and z-axes respectively. Then, \(\cos^2\alpha + \cos^2\beta + \cos^2\gamma\) is equal to

• A. \(1/2\)
• B. \(-1/2\)
• C. \(-1\)
• D. 1

Hint:

Direction cosines: \(l = \cos\alpha, m = \cos\beta, n = \cos\gamma\), with \(l^2 + m^2 + n^2 = 1\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Direction cosines satisfy \(l^2 + m^2 + n^2 = 1\).
Step 2: Detailed Explanation:
\(\cos\alpha, \cos\beta, \cos\gamma\) are direction cosines, so
\(\cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1\)
Step 3: Final Answer:
1.