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JEE Main Math Class 12 Vector Algebra Part 2 Questions
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© examsnet.com
Question : 3
Total: 100
The foot of perpendicular from the origin
O
to a plane
P
which meets the co-ordinate axes at the points
A
,
B
,
C
is
(
2
,
a
,
4
)
,
a
∈
N
. If the volume of the tetrahedron
OABC
is
144
unit
3
, then which of the following points is NOT on P?
[31-Jan-2023 Shift 2]
(
2
,
2
,
4
)
(
0
,
4
,
4
)
(
3
,
0
,
4
)
(
0
,
6
,
3
)
Validate
Solution:
Equation of Plane:
(
2
^
i
+
a
^
j
+
4
^
k
)
⋅
[
(
x
−
2
)
^
i
+
(
y
−
a
)
^
j
+
(
z
−
4
)
^
k
]
=
0
⇒
2
x
+
ay
+
4
z
=
20
+
a
2
⇒
A
≡
(
20
+
a
2
2
,
0
,
0
)
B
≡
(
0
,
20
+
a
2
a
,
0
)
C
≡
(
0
,
0
,
20
+
a
2
4
)
⇒
Volume of tetrahedron
=
1
6
[
→
a
→
b
→
c
]
=
1
6
→
a
.
(
→
b
×
→
c
)
⇒
1
6
(
20
+
a
2
2
)
⋅
(
20
+
a
2
a
)
⋅
(
20
+
a
2
4
)
=
144
⇒
(
20
+
a
2
)
3
=
144
×
48
×
a
⇒
a
=
2
⇒
Equation of plane is
2
x
+
2
y
+
4
z
=
24
Or
x
+
y
+
2
z
=
12
⇒
(
3
,
0
,
4
)
Not lies on the Plane
x
+
y
+
2
z
=
12
© examsnet.com
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