Question

The direction ratios of the $x$-axis are

• A. $(0,k,0)$
• B. $(0,0,k)$
• C. $(k,0,0)$
• D. $(k,k,k)$

Hint:

A line parallel to the $x$-axis has direction ratios proportional to $(1,0,0)$.

Answer 1

The Correct Option is C

Step 1: Recall the concept of direction ratios.
Direction ratios of a line are numbers proportional to the components of a vector that represents the direction of the line.
If a line is parallel to the $x$-axis, its direction is completely along the $x$-direction.

Step 2: Determine the components of the direction vector.
For a line along the $x$-axis: \[ x \text{-direction component} \neq 0 \] \[ y \text{-direction component} = 0 \] \[ z \text{-direction component} = 0 \] Thus a direction vector along the $x$-axis can be written as \[ (1,0,0) \]
Step 3: Express general direction ratios.
Direction ratios can be any proportional values of the direction vector. Therefore the general form becomes \[ (k,0,0) \] where \(k\) is any non-zero scalar.

Step 4: Conclusion.
Hence the direction ratios of the $x$-axis are $(k,0,0)$.
Final Answer: $\boxed{(k,0,0)}$