Equation Of A Plane

1. Analyze the equation :

In three-dimensional space, implies either or .

2. Interpret geometrically:

represents the -plane, and represents the -plane. These two planes intersect at the -axis and are perpendicular to each other.

3. Match the result to the options:

The equation represents a pair of perpendicular planes, corresponding to option (C).

Correct Answer: (C) A pair of planes at right angles

1. Identify the point and line:

The plane must contain the point and the line .

2. Find two points on the line:

For : (given).

For : .

3. Compute two vectors in the plane:

Vector from to : .

Vector from to : .

4. Find the normal vector to the plane:

Compute the cross product :

Simplify to .

5. Write the plane equation:

Using point and normal vector :

Correct Answer: (A)