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Mathematics · JEE | THREE DIMENSIONAL GEOMETRY

हिन्दी

Match List-I with List-II: List-I (Line Orientation) List-II (Direction Cosines) A Line along positive \( x \)-axis I \( (\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}) \) B Line along positive \( y \)-axis II \( (1, 0, 0) \) C Line along positive \( z \)-axis III \( (0, 1, 0) \) D Line equally inclined to coordinate axes in the positive octant IV \( (0, 0, 1) \) Choose the correct answer from the options given below:

Match List-I with List-II:

List-I (Line Orientation) List-II (Direction Cosines)
A Line along positive \( x \)-axis I \( (\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}) \)
B Line along positive \( y \)-axis II \( (1, 0, 0) \)
C Line along positive \( z \)-axis III \( (0, 1, 0) \)
D Line equally inclined to coordinate axes in the positive octant IV \( (0, 0, 1) \)

Choose the correct answer from the options given below:

  1. A
    A-(II), B-(III), C-(IV), D-(I)
  2. B
    A-(III), B-(II), C-(IV), D-(I)
  3. C
    A-(II), B-(IV), C-(III), D-(I)
  4. D
    A-(I), B-(III), C-(IV), D-(II)
View Answer & Solution

Correct answer · Option A

A-(II), B-(III), C-(IV), D-(I)

Explanation

The d.c.'s of x-axis are (1,0,0), y-axis are (0,1,0), z-axis are (0,0,1), and an equally inclined line in the positive octant has d.c.'s \( (1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3}) \).
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