Vectors of field type real numbers are difficult to visualize if *n* is not 1,2, or 3. Familiar objects like lines and planes make sense for any value of *n*. Line *L* along the direction defined by a vector *v*, through a point *P* labeled by a vector u, can be written as follows:

*L = {u + tv | t* *∈ R}*

Given two non-zero vectors, *u* and *v*, they determine a plane if both the vectors are not in the same line, and one of the vectors is a scalar multiple of the other. The addition of two vectors is accomplished by laying the vectors head to tail in a sequence to create a triangle. If u and *v* lie in a plane, then their sum lies in the plane of *u* and *v*. The plane represented by two vectors *u* and *v* can be mathematically shown as follows:

*{P ...*