EQUATION OF LINE

 

 

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.