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JEE Main Math Class 12 Three Dimensional Geometry Part 2 Questions
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© examsnet.com
Question : 2
Total: 100
If the mirror image of the point
(
2
,
4
,
7
)
in the plane
3
x
−
y
+
4
z
=
2
is
(
a
,
b
,
c
)
, then
2
a
+
b
+
2
c
is equal to:
[29-Jun-2022-Shift-1]
54
50
−
6
−
42
Validate
Solution:
We know mirror image of point
(
x
1
,
y
1
,
z
1
)
in the plane
ax
+
by
+
cz
=
d
x
−
x
1
a
=
y
−
y
1
b
=
z
−
z
1
c
=
−
2
(
a
x
1
+
b
y
1
+
c
z
1
−
d
)
a
2
+
b
2
+
c
2
Here given point
(
2
,
4
,
7
)
and plane
3
x
−
y
+
4
z
=
2
then mirror image is
x
−
2
3
=
y
−
4
−
1
=
z
−
7
4
=
−
2
(
6
−
4
+
28
−
2
)
9
+
1
+
16
⇒
x
−
2
3
=
y
−
4
−
1
=
z
−
7
4
=
−
28
13
∴
x
=
−
58
13
=
a
y
=
80
13
=
b
z
=
−
21
13
=
c
∴
2
a
+
b
+
2
c
=
2
(
−
58
13
)
+
80
13
+
2
(
−
21
13
)
=
−
116
+
80
−
42
13
=
−
78
13
=
−
6
© examsnet.com
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