PROBLEMS
10

SPHERE
Page
1
( 1 )
Find
the
equations
in
vector
as
well
as
Cartesian
form
of
a
sphere
with
centre
( 2,
3,
4 )
and
passing
through
( 4,
4,
4 ).
[ Ans:
l
r
l
2

2 ( 2,
3,
4 )
r
⋅
+
24
=
0,
x
2
+
y
2
+
z
2

4x

6y

8z
+
24
=
0 ]
( 2 )
Find
the
centre
and
length
of
radius
of
the
sphere
2
r

r
⋅
( 3,
1,
 1 )
+
2
=
0.
2
3
,
2
1
,
2
1
,
2
3
:
Ans

( 3 )
Find
the
centre
and
radius
of
the
sphere
represented
by
2x
2
+
2y
2
+
2z
2

4x
+
1
=
0.
2
1
),
0
0,
1,
(
:
Ans
( 4 )
Obtain
the
equation,
the
centre
and
length
of
a
radius
of
the
sphere
through
( 0,
0,
0 ),
( a,
0,
0 ),
( 0,
b,
0 )
and
( 0,
0,
c ).
+
+
+
+
=
c
b
a
2
1
0,
cz
by
ax
z
y
x
:
Ans
2
2
2
2
2
2



( 5 )
If
the
diameter
of
the
sphere
has
endpoints
( 1,
2,
 1 )
and
( 2,
1,
0 ),
obtain
the
equation
of
the
sphere.
[ Ans:
x
2
+
y
2
+
z
2

3x

3y
+
z
+
4
=
0 ]
( 6 )
Derive
the
equation
of
the
sphere
through
( 0,
0,
0 ),
(  a,
b,
c ),
( a,
 b,
c )
and
( a,
b,
 c ).
+
+
+
+
+
+
c