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The direction cosines l, m, n of one of the two lines satisfying the relations l - 5m + 3n = 0 and 7l² + 5m² - 3n² = 0 are
- 1/√14, 2/√14, 3/√14
- −1/√14, 2/√14, 3/√14
- 1/√14, −2/√14, 3/√14
- 1/√14, 2/√14, −3/√14
Correct answer: 1/√14, 2/√14, 3/√14
Solution
The correct option satisfies both given equations for direction cosines, ensuring they maintain the necessary relationships between l, m, and n while also adhering to the constraint that the sum of the squares of the direction cosines equals 1.
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- Consider the following two statements:
Statement 1: If A, B and C are points with position vectors a = 2î + ĵ + k̂, b = 3î - ĵ + 3k̂ and c = î + 7ĵ - 5k̂, then the figure OABC forms a tetrahedron.
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