Vector Equation of a Line

A line is defined as the set of alligned points on the plane with a point, P, and a directional vector, Vector.

Direction Vector

If P(x1, y1) is a point on the line and the vector Vector has the same direction as Vector, then Vector equals Vector multiplied by a scalar unit:

Direction Vector

Direction Vector

Direction Vector

Direction Vector

Examples

A line passes through point A = (−1, 3) and has a directional vector Vector with components (2, 5). Determine the equation of the vector.

Vector Equation Example


Write the vector equation of the line which passes through the points A = (1, 2) and B = (−2, 5).

Vector Equation Example

Vector Equation Solution