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Byju's Answer
Standard XII
Mathematics
Shortest Distance between Two Skew Lines
The shortest ...
Question
The shortest distance between the lines
x
−
y
=
0
=
2
x
+
z
and
x
+
y
−
2
=
0
=
3
x
−
y
+
z
−
1
is
A
1
√
11
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B
1
2
√
3
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C
1
2
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D
1
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Solution
The correct option is
D
1
√
11
L
1
:
x
−
y
=
0
=
2
x
+
z
and
L
2
:
x
+
y
−
2
=
0
=
3
x
−
y
+
z
−
1
It can also be write as
L
1
:
x
1
=
y
1
=
z
−
2
L
2
:
x
−
1
=
y
−
2
1
=
z
−
3
4
A
(
0
,
0
,
0
)
be the point on
L
1
and
→
B
=
(
^
i
+
^
j
−
2
^
k
)
is a direction of
L
1
C
(
0
,
2
,
3
)
be the point on
L
2
and
→
D
=
(
−
^
i
+
^
j
+
4
^
k
)
is a direction of
L
2
→
B
×
→
D
=
6
^
i
−
2
^
j
+
2
^
k
∣
∣
→
B
×
→
D
∣
∣
=
√
6
2
+
2
2
+
2
2
=
2
√
11
→
C
−
→
A
=
2
^
j
+
3
^
k
(
→
B
×
→
D
)
.
(
→
C
−
→
A
)
=
(
6
^
i
−
2
^
j
+
2
^
k
)
⋅
(
2
^
j
+
3
^
k
)
=
2
The shortest distance between line
L
1
and
L
2
can bee found using the following formula.
Distance
=
∣
∣ ∣
∣
→
B
×
→
D
|
→
B
×
→
D
|
.
(
→
C
−
→
A
)
∣
∣ ∣
∣
Distance
=
1
√
11
Hence, option A.
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Similar questions
Q.
The shortest distance between the lines
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and
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Q.
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)
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Q.
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