Equation of plane passing through P(a,b,c) and parallel to xy plane is

Options

A. x=a
B. y=b
C. z=c
D. None of these

Answer

To find the equation of a plane that passes through the point \( P(a, b, c) \) and is parallel to the XY plane, we can follow these steps:

### Step 1: Understand the properties of the plane
A plane that is parallel to the XY plane will have a constant Z-coordinate. This means that no matter what values X and Y take, Z will always remain the same.

**Hint:** Remember that parallel planes share the same normal vector. The normal vector for the XY plane is along the Z-axis.

### Step 2: Identify the point through which the plane passes
The plane passes through the point \( P(a, b, c) \). This point gives us the specific Z-coordinate that the plane will maintain.

**Hint:** The coordinates of point P are crucial as they define the position of the plane in 3D space.

### Step 3: Write the equation of the plane
Since the plane is parallel to the XY plane, the equation of the plane can be expressed as:
\[ z = c \]
This indicates that for any point \( (x, y, z) \) on the plane, the Z-coordinate will always be equal to \( c \).

**Hint:** The equation \( z = c \) signifies that the plane extends infinitely in the X and Y directions while maintaining a constant Z value.

### Final Answer
Thus, the equation of the plane passing through the point \( P(a, b, c) \) and parallel to the XY plane is:
\[ z = c \]