For a vector space over a field F these n-tuples form the vector space (where the operation are pointwise addition and scalar multiplication). Displacement vector a vector that specifies the change in position of a point relative to a previous position. Displacement vectors belong to the vector space of translations.So the vectors arent parallel and so the plane and the line are not orthogonal. Now lets check to see if the plane and line are parallel. If the line is parallel to the plane then any vector parallel to the line will be orthogonal to the normal vector of the plane. In other words if (vec n) and (vec vA plane is the two-dimensional analogue of a point (zero dimensions) a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space as with a rooms walls extended infinitely far or they may enjoy an independent existence in their own right as in the setting of Euclidean geometry.
We use the notation v v to denote the magnitude of the vector v. v. A vector with an initial point and terminal point that are the same is called the zero vector denoted 0. 0. The zero vector is the only vector without a direction and by convention can be considered to have any direction convenient to the problem at hand.