PROBLEMS
09

PLANE
Page
1
( 1 )
Obtain
the
vector
and
Cartesian
equations
of
the
plane
through
A ( 1,
2,
3 ),
B ( 2,
1,
0 )
and
C ( 3,
3,
 1 ).
[ Ans:
r
=
( 1,
2,
3 )
+ m ( 1,
 1,
 3 )
+
n ( 2,
1,
 4 ),
7x

2y
+
3z
=
12 ]
( 2 )
A
plane
intersects
X,
Y
and
Zaxes
at
A,
B
and
C
respectively.
The
centroid
of
triangle
ABC
is
( p,
q,
r ).
Derive
the
equation
of
the
plane.
+
+
=
3
r
z
q
y
p
x
:
Ans
( 3 ) Obtain
the
foot
of
perpendicular
from
the
point
( 1,
2,
3 )
on
the
plane
x

2y
+
2z
=
5
and
the
distance
of
the
point
from
the
plane.
3
2
,
9
31
,
9
14
,
9
11
:
Ans
( 4 )
Find
the
image
of
( 1,
3,
4 )
relative
to
the
plane
2x

y
+
z
+
3
=
0.
[ Ans:
(  3,
5,
2 ) ]
( 5 )
Find
the
common
section
of
x
+
2y

3z
=
6
and
2x

y
+
z
=
7.
=
=
5
z
7
1
y
1
4
x
:
Ans


( 6 )
Obtain
the
equation
of
the
plane
through
( 1,
3,
5 )
perpendicular
to
the
intersection
of
3x
+
y

z
=
0
and
x
+
2y
+
3z
=
5.
[ Ans: