Question 22 of 25beginner💡 UnderstandVery Short2 marks

Find the equation of a line parallel to xx-axis and passing through the origin.

Correct Answer

The equation of the line is y = 0, z = 0. In symmetric form, it can be written as x/1 = y/0 = z/0.

Exercise: Miscellaneous Exercise on Chapter 11 | Q: 2 | (Page Page 14)
For More Understanding

Explanation

The line parallel to the x-axis has direction cosines (1, 0, 0). Since it passes through the origin (0,0,0), using the formula (x - x₁)/l = (y - y₁)/m = (z - z₁)/n, we substitute x₁=0, y₁=0, z₁=0 and l=1, m=0, n=0. This gives x/1 = y/0 = z/0, which implies y=0 and z=0. Thus, the line is the x-axis itself.

Solution Steps

  1. Step 1: Identify direction cosines of a line parallel to x-axis: l=1, m=0, n=0.

  2. Step 2: The line passes through origin, so point is (0,0,0).

  3. Step 3: Apply the formula (x - x₁)/l = (y - y₁)/m = (z - z₁)/n to get x/1 = y/0 = z/0.

  4. Step 4: Interpret the equation: y/0 and z/0 indicate y=0 and z=0, giving the final equations y=0, z=0.

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