Question

The Cartesian equations of the line passing through \(A(0,1,1)\) and parallel to the X-axis are ....

• A. \(y = 1,z = 1\)
• B. \(x = 0\)
• C. \(x+y+z = 2\)
• D. \(y = z\)

Hint:

A line parallel to the x-axis keeps y and z fixed.

Answer 1

The Correct Option is A

Step 1: Approach
Use the parametric form.

Step 2: Parametric
$(x,y,z)=(0,1,1)+t(1,0,0)=(t,1,1)$.

Step 3: Eliminate t
$y=1$ and $z=1$ for all $t$, with $x$ free. So the Cartesian equations are $y=1,\ z=1$, option (A).

Final Answer:
A line parallel to the X-axis through (0, 1, 1) is y = 1 and z = 1, option (A). \[ \boxed{y=1,\ z=1} \]