In three-dimensional space, we often need to calculate the shortest distance from a point to a plane. This distance is the length of the perpendicular line segment from the point to the plane.To calculate the distance from a point to a plane, we first need to understand how a plane is defined in three-dimensional space. A plane can be represented by the equation ax + by + cz + d = 0, where (a, b, c) forms the normal vector to the plane, and d is a constant.The formula for calculating the distance from a point to a plane is D equals the absolute value of ax zero plus by zero plus cz zero plus d, divided by the square root of a squared plus b squared plus c squared. This formula essentially measures how far the point is from satisfying the plane equation, normalized by the magnitude of the plane's normal vector.Let's work through an example. We'll find the distance from point P with coordinates (1, 2, 3) to the plane defined by 2x minus 3y plus 6z minus 8 equals zero. First, we identify the coefficients: a equals 2, b equals negative 3, c equals 6, and d equals negative 8. Then we plug these values and the point coordinates into our distance formula.Now let's calculate step by step. First, we identify the coefficients from the plane equation: a equals 2, b equals negative 3, c equals 6, and d equals negative 8. Next, we use the point coordinates x zero equals 1, y zero equals 2, and z zero equals 3. For the numerator, we compute the absolute value of 2 times 1 plus negative 3 times 2 plus 6 times 3 plus negative 8, which equals the absolute value of 6, or 6. For the denominator, we calculate the square root of 2 squared plus negative 3 squared plus 6 squared, which is the square root of 49, or 7. Therefore, the distance D equals 6 over 7.