EQUATION OF A LINE IN A PLANE:
The parametric equation of a straight line in a plane:
x = x0 + a.t
y = y0 + b.t
(x, y) and (x0, y0) are the position vectors
(a, b) is the direction vector. Slope = b/a
The vector equation of a straight line in a plane:
r = (x0, y0) + t (a, b)
(x, y) and x = (x0, y0) are the position vectors
(a, b) is the direction vector. Slope = b/a
The scalar or Cartesian equation of a straight line in a plane:
Ax +By + C = 0
Direction of the normal to the line: (A, B)
NOTE: There is no scalar equation of a line in space because it has no unique normal.
The distance from the point (x1, y1) to the line Ax +By + C = 0
EQUATION OF A LINE IN 3 - SPACE:
The vector equation of a straight line in a space:
r = (x0, y0, y0) + t (a, b, c)
(x, y, z) and (x0, y0, y0) are the position vectors
(a, b, c) is the direction vector. Slope = b/a
The parametric equation of a straight line in a space:
x = x0 + a.t
y = y0 + b.t
z = z0 + c.t
(x0, y0, y0) are the coordinates of some point on the line.
(a, b, c) is the direction vector.
The symmetric equation of a straight line in a space:
(x0, y0, y0) are the coordinates of some point on the line.
(a, b, c) is the direction vector.