MTH 254 Vector-Valued Functions: Lines
Vector Form of a Line
A line in three-space can be created through a specific point to extend in a particular direction by using scalar multiplication and vector addition.
When a position vector is added to scalar multiples of a direction vector, the components of the resultant vectors form the set of points making up the line. Initially, a point on the line determines the components of the position vector. A vector parallel to the line is chosen to be the "direction" vector.
Interactive Graph:
- Interact with the graph by adjusting the coordinates of points A and B.
- The position vector in red is and is labeled as a.
- The direction vector in blue is and is labeled as b.
- The parameter is , which can be varied using the slider.
- As the parameter λ changes, = a + λb traces out a line.