Mostafa Mahmoud Sabri
This section is specifically concerned with planes embedded in three dimensions: specifically, in R3. Properties[edit source | editbeta] In three-dimensional Euclidean space, we may exploit the following facts that do not hold in higher dimensions: Two planes are either parallel or they intersect in a line. A line is either parallel to a plane, intersects it at a single point in three-dimensional space, or is contained in the plane. Two lines perpendicular to the same plane must be parallel to each other. Two planes perpendicular to the same line must be parallel to each other. Definition with a point and a normal vector[edit source | editbeta] In a three-dimensional space, another important way of defining a plane is by specifying a point and a normal vector to the plane. Let r0 be the position vector of some known point P_0 in the plane, and let n be a nonzero vector normal to the plane. The idea is that a point P with position vector r is in the plane if and only if the vec
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