The coordinates of the foot of a perpendicular drawn from the origin to the plane are (2, 3, 1). Find the equation of the plane in vector form.

Explanation

To find the equation of the plane in vector form given the foot of the perpendicular from the origin to the plane at the point (2, 3, 1), we can follow these steps:

### Step 1: Identify the point and normal vector
The coordinates of the foot of the perpendicular from the origin to the plane are given as \( R_0 = (2, 3, 1) \). This point lies on the plane.

The vector from the origin (0, 0, 0) to the point (2, 3, 1) is the normal vector \( \mathbf{N} \) of the plane. We can express this vector as:
\[
\mathbf{N} = 2\mathbf{i} + 3\mathbf{j} + 1\mathbf{k}
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