Final answer:
The distance between two parallel planes is calculated using the magnitude of the normal vector. It involves the scalar product of the direction vector and the normal vector of the planes. The correct answer to the multiple-choice question is A) magnitude of the normal vector.
Step-by-step explanation:
The distance between two given parallel planes can be found using the direct distance formula derived from the scalar product (dot product) of normal vectors. To find the distance, we take the absolute value of the scalar product of the direction vector of one plane and a normal vector of another plane, normalized by the magnitude of the normal vector. Note that the normal vectors are perpendicular to the planes and hence parallel to each other.
Using the scalar product, the distance is the component of the direction vector along the normal vector, which can also be expressed as an orthogonal projection of one vector onto another. Practically, the distance is calculated as the absolute difference in perpendicular displacements of the planes from the origin along the normal direction.
The correct choice from the multiple-choice questions provided would be A) magnitude of the normal vector, because the distance is equal to the component of the direction vector along the normal vector, which is the magnitude of that component.