Given an 
-dimensional space, the standard form of an equation for that space is given by the following:
As mentioned in the last subsection, 
equations are required to specify an object of 
dimensions. So in 
a single equation of the form 
is the standard form of a line. This form can be obtained by finding the sloper-intercept form (
) and rearranging it to standard form.
In
a single equation of the form 
is the standard form of a plane. If a plane is seen as an infinite set of vectors, all the vectors in a plane can be represented by the following:
These vectors all start at the point 
. Although there are an infinite number of vectors from this point, there is only 1 vector, called the normal vector 
, that is perpendicular to all of them. The normal along with 
uniquely defines the plane. Since the dot product 
because 
is perpendicular to all 
we find the following:
If we set the right-hand side 
equal to 
we have the standard equation of the plane. So how do we find the normal? We simply need to cross two vectors that are in the plane.
-dimensional space, the standard form of an equation for that space is given by the following: equations are required to specify an object of dimensions. So in a single equation of the form is the standard form of a line. This form can be obtained by finding the sloper-intercept form () and rearranging it to standard form. In
a single equation of the form is the standard form of a plane. If a plane is seen as an infinite set of vectors, all the vectors in a plane can be represented by the following:. Although there are an infinite number of vectors from this point, there is only 1 vector, called the normal vector , that is perpendicular to all of them. The normal along with uniquely defines the plane. Since the dot product because is perpendicular to all we find the following: equal to we have the standard equation of the plane. So how do we find the normal? We simply need to cross two vectors that are in the plane.