Different
forms of Equation of a plane
We have already seen the notion of a plane.
Definition 6.8
A straight line which is perpendicular to a plane is called a normal to the plane.
Note
Every normal to a plane is perpendicular to every straight line
lying on the plane.
A plane is uniquely fixed if any one of the following is given:
·
a unit normal to the plane and the distance of the plane from
the origin
·
a point of the plane and a normal to the plane
·
three non-collinear points of the plane
·
a point of the plane and two non-parallel lines or non-parallel
vectors which are parallel to the plane
·
two distinct points of the plane and a straight line or non-zero
vector parallel to the plane but not parallel to the line joining the two
points.
Let us find the vector and Cartesian equations of planes using
the above situations.
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