Mathematics · JEE | THREE DIMENSIONAL GEOMETRY
हिन्दीMatch 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:
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 \( (1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3}) \).