These planes will resemble the pages of a book where the
line containing the points R, S and T are members in the binding
of the book Cartesian form
Let (x1, y1, z1), (x2, y2, z2) and (x3,  y3,  z3) be the coordinates of the points R, S and T
respectively Let (x, y, z) be the coordinates of any point P on the plane with position
vector rr Then
RP
uuur  = (x – x1) ˆi  + (y – y1) ˆj  + (z – z1) ˆk
RS
uuur  = (x2 – x1) ˆi  + (y2 – y1) ˆj  + (z2 – z1) ˆk
RT
uuur  = (x3 – x1) ˆi + (y3 – y1) ˆj  + (z3 – z1) ˆk
Substituting these values in equation (1) of the vector form and expressing it in the
form of a determinant, we have
1
1
1
2
1
2
1
2
1
3
1
3
1
3
1
0
x
x
y
y
z
z
x
x
y
y
z
z
x
x
y
y
z
z
−
−
−
−
−
−
=
−
−
−
which is the equation of the plane in Cartesian form passing through three non collinear
points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3)