Question

The straight line \[ \frac{x-3}{3} = \frac{y-2}{1} = \frac{z-1}{0} \] is:

• A. parallel to the x-axis.
• B. parallel to the y-axis.
• C. parallel to the z-axis.
• D. perpendicular to the z-axis.

Hint:

For symmetric line equations: \begin{itemize} \item Direction ratios come from denominators. \item Zero denominator ⇒ coordinate constant. \end{itemize}

Answer 1

The Correct Option is C

Concept: In symmetric form: \[ \frac{x-x_1}{l} = \frac{y-y_1}{m} = \frac{z-z_1}{n} \] Direction ratios are \( (l,m,n) \). Step 1: {\color{red}Identify direction ratios.} Given: \[ \frac{x-3}{3} = \frac{y-2}{1} = \frac{z-1}{0} \] Direction ratios: \[ (3,1,0) \] Step 2: {\color{red}Interpret zero component.} Since direction ratio along \( z \) is zero, line has no movement in \( z \)-direction. So it lies parallel to plane of constant \( z \). Step 3: {\color{red}Geometric interpretation.} Line remains at fixed \( z=1 \) and varies in x-y plane. Thus it is parallel to z-axis.