� Equation of a plane which is at a distance of d from the origin and the direction
cosines of the normal to the plane as l, m, n is lx + my + nz = d � The equation of a plane through a point whose position vector is ar  and
perpendicular to the vector N
ur
 is (
) N
0
r
−a
=
ur
r
r � Equation of a plane perpendicular to a given line with direction ratios A, B, C
and passing through a given point (x1, y1, z1) is
A (x – x1) + B (y – y1) + C (z – z1 ) = 0
� Equation of a plane passing through three non collinear points (x1, y1, z1),
© NCERT
not to be republished
 MATHEMATI CS
502
(x2, y2, z2) and (x3, y3, z3) is
1
3
1
3
1
3
1
2
1
2
1
2
1
1
1
z
z
y
y
x
x
z
z
y
y
x
x
z
z
y
y
x
x
−
−
−
−
−
−
−
−
−
 = 0
� Vector equation of a plane that contains three non collinear points having
position vectors 
b
a
r,r
 and cr is  (
)