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JEE Main 28 June 2022 Shift 2 Solved Paper
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© examsnet.com
Question : 21
Total: 90
Let the image of the point
P
(
1
,
2
,
3
)
in the line
L
:
x
−
6
3
=
y
−
1
2
=
z
−
2
3
be Q. Let
R
(
α
,
β
,
γ
)
be a point that divides internally the line segment
P
Q
in the ratio
1
:
3
. Then the value of
22
(
α
+
β
+
γ
)
is equal to___
[28-Jun-2022-Shift-2]
Your Answer:
Validate
Solution:
The point dividing
P
Q
in the ratio
1
:
3
will be mid-point of
P
&
foot of perpendicular from
P
on the line.
∴
Let a point on line be
λ
⇒
x
−
6
3
=
y
−
1
2
=
z
−
2
3
=
λ
⇒
P
′
(
3
λ
+
6
,
2
λ
+
1
,
3
λ
+
2
)
as
P
′
is foot of perpendicular
(
3
λ
+
5
)
3
+
(
2
λ
−
1
)
2
+
(
3
λ
−
1
)
3
=
0
⇒
22
λ
+
15
−
2
−
3
=
0
⇒
λ
=
−
5
11
∴
P
′
(
51
11
,
1
11
,
7
11
)
Mid-point of
P
P
′
≡
(
51
11
+
1
2
,
1
11
+
2
2
,
7
11
+
3
2
)
≡
(
62
22
,
23
22
,
40
22
)
≡
(
α
,
β
,
γ
)
⇒
22
(
α
,
β
,
γ
)
=
62
+
23
+
40
=
125
© examsnet.com
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