Question

The equation of the plane passing through the points \( (2, 3, 1), (4, -5, 3) \) and parallel to the y-axis is

• A. \( x + z = 3 \)
• B. \( x + z = 1 \)
• C. \( x - z = 1 \)
• D. \( z - x + 2 = 0 \)

Hint:

For a plane parallel to the y-axis, the \( y \)-component will not appear in the equation.

Answer 1

The Correct Option is C

Step 1: Use the given points and the condition of parallelism to the y-axis.
To find the equation of the plane, first calculate the direction ratios of the two points given: \[ \text{Direction ratios} = (4 - 2, -5 - 3, 3 - 1) = (2, -8, 2) \] Since the plane is parallel to the y-axis, the direction ratio along \( y \) is zero.
Step 2: Write the equation of the plane.
The equation of the plane is given by: \[ x - z = 1 \] This corresponds to option (C).