EQUATION OF LINE
EQUATION OF A LINE IN A PLANE:
The parametric equation of a straight line in a plane:
x = x_{0} + a.t y = y_{0} + b.t
(x, y) and (x_{0}, y_{0}) are the position vectors (a, b) is the direction vector. Slope = b/a
The vector equation of a straight line in a plane:
r = (x_{0}, y_{0}) + t (a, b)
(x, y) and x = (x_{0}, y_{0}) 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 (x_{1}, y_{1}) 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 = (x_{0}, y_{0},_{ }y_{0}) + t (a, b, c)
(x, y, z) and (x_{0}, y_{0},_{ }y_{0}) 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 = x_{0} + a.t y = y_{0} + b.t z = z_{0} + c.t
(x_{0}, y_{0},_{ }y_{0}) 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: _{ } _{ }
(x_{0}, y_{0},_{ }y_{0}) are the coordinates of some point on the line. (a, b, c) is the direction vector. |