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Test Index
JEE Main Math Class 12 Three Dimensional Geometry Part 3 Questions
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© examsnet.com
Question : 42
Total: 134
Let the line of the shortest distance between the lines
L
1
:
→
r
=
(
^
i
+
2
^
j
+
3
^
k
)
+
λ
(
^
i
−
^
j
+
^
k
)
and
L
2
:
→
r
=
(
4
^
i
+
5
^
j
+
6
^
k
)
+
µ
(
^
i
+
^
j
−
^
k
)
intersect
L
1
and
L
2
at
P
and
Q
respectively. If
(
α
,
β
,
γ
)
is the midpoint of the line segment PQ, then
2
(
α
+
β
+
γ
)
is equal to____
[1-Feb-2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
→
b
=
^
i
−
^
j
+
^
k
(
DR's of
L
1
)
→
d
=
^
i
+
^
j
−
^
k
(
D
R
′
s
of
L
2
)
→
b
×
→
d
=
|
^
i
^
j
^
k
1
−
1
1
1
1
−
1
|
=
0
^
i
+
2
^
j
+
2
^
k
(DR's of Line perpendicular to
L
1
and
L
2
)
DR
of
AB
line
=
(
0
,
2
,
2
)
=
(
3
+
µ
−
λ
,
3
+
µ
+
λ
,
3
−
µ
−
λ
)
3
+
µ
−
λ
0
=
3
+
µ
+
λ
2
=
3
−
µ
−
λ
2
Solving above equation we get
µ
=
−
3
2
and
λ
=
3
2
point
A
=
(
5
2
,
1
2
,
9
2
)
B
=
(
5
2
,
7
2
,
15
2
)
Point of
AB
=
(
5
2
,
2
,
6
)
=
(
α
,
β
,
γ
)
2
(
α
+
β
+
γ
)
=
5
+
4
+
12
=
21
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