Exponential And Logarithmic Functions

To solve the problem, we need to find the equation of a plane given the foot of the perpendicular from the origin to the plane.

1. Identify the Given Information:
Let the plane be denoted as and the origin as .
The foot of the perpendicular from the origin to the plane is .

2. Determine the Normal’s Direction Ratios:
The direction ratios of the normal to the plane are given by the coordinates of , which are .

3. Form the Plane Equation:
The equation of the plane is of the form , where is a constant.
Since lies on the plane, substitute its coordinates into the equation:


.

4. Write the Final Equation:
The equation of the plane is , or .

Final Answer:
The equation of the plane is .