LCKurtz said:
A vector equation of planes is a mathematical representation of a plane in three-dimensional space using vectors. It allows us to describe the position and orientation of a plane in terms of its normal vector and a point on the plane.
A scalar equation of planes is a mathematical representation of a plane using only scalar quantities, such as coefficients and constants. A vector equation of planes, on the other hand, uses vectors to describe the position and orientation of a plane. This makes it more versatile and allows for more complex calculations.
The normal vector in a vector equation of planes can be determined by taking the cross product of two non-parallel vectors that lie in the plane. The resulting vector will be perpendicular to the plane and thus, the normal vector.
Yes, a vector equation of planes can be used to find the distance between two planes. This can be done by finding the shortest distance between a point on one plane and the other plane, using the normal vector of each plane.
Yes, it is possible for two planes to be parallel, but not equal, in a vector equation of planes. This means that they have the same normal vector, but different points on the plane. In this case, the planes will never intersect.
