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Mathematics · JEE | THREE DIMENSIONAL GEOMETRY
हिन्दीMatch List-I with List-II: List-I (Given Data) List-II (Magnitude of Direction Cosine \( |l| \)) A Line with direction ratios \( -18, 12, -4 \) I \( \frac{3}{\sqrt{77}} \) B Line with direction ratios \( 2, -1, -2 \) II \( \frac{9}{11} \) C Line passing through \( (-2, 4, -5) \) and \( (1, 2, 3) \) III \( \frac{2}{3} \) D Line equally inclined to the three coordinate axes IV \( \frac{1}{\sqrt{3}} \) Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I (Given Data) | List-II (Magnitude of Direction Cosine \( |l| \)) | ||
|---|---|---|---|
| A | Line with direction ratios \( -18, 12, -4 \) | I | \( \frac{3}{\sqrt{77}} \) |
| B | Line with direction ratios \( 2, -1, -2 \) | II | \( \frac{9}{11} \) |
| C | Line passing through \( (-2, 4, -5) \) and \( (1, 2, 3) \) | III | \( \frac{2}{3} \) |
| D | Line equally inclined to the three coordinate axes | IV | \( \frac{1}{\sqrt{3}} \) |
Choose the correct answer from the options given below:
View Answer & Solution
Correct answer · Option B
A-(II), B-(III), C-(I), D-(IV)
Explanation
For A: \( \sqrt{18^2+12^2+4^2} = \sqrt{324+144+16} = 22 \implies |l| = 18/22 = 9/11 \). For B: \( |l| = 2/3 \). For C: \( |l| = 3/\sqrt{77} \). For D: \( |l| = 1/\sqrt{3} \).
