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
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
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Direction cosines: \(l = \cos\alpha, m = \cos\beta, n = \cos\gamma\), with \(l^2 + m^2 + n^2 = 1\).
Updated On: Apr 7, 2026
- \(1/2\)
- \(-1/2\)
- \(-1\)
- 1
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The Correct Option is D
Solution and Explanation
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.
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.
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