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Byju's Answer
Standard XII
Mathematics
Angle between Two Line Segments
If the lines ...
Question
If the lines
x
−
1
2
=
y
+
1
3
=
z
−
1
4
and
x
−
3
1
=
y
−
k
2
=
z
1
intersect, then find the value of k.
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Solution
The equations of the given lines are
x
−
1
2
=
y
+
1
3
=
z
−
1
4
and
x
−
3
1
=
y
−
k
2
=
z
1
∴
x
1
=
1
,
y
1
=
−
1
,
z
1
=
1
,
x
2
=
3
,
y
2
=
k
,
z
2
=
0
l
1
=
2
,
m
1
=
3
,
n
1
=
4
,
l
2
=
1
,
m
2
=
2
,
n
2
=
1
Since these lines intersect each other, we get
∣
∣ ∣
∣
x
2
−
x
1
y
2
−
y
1
z
2
−
z
1
l
1
m
1
n
1
l
2
m
2
n
2
∣
∣ ∣
∣
=
0
∣
∣ ∣
∣
2
k
+
1
−
1
2
3
4
1
2
1
∣
∣ ∣
∣
=
0
⇒
2
(
3
−
8
)
−
(
k
+
1
)
(
2
−
4
)
−
1
(
4
−
3
)
=
0
⇒
−
10
+
2
k
+
2
−
1
=
0
⇒
2
k
=
9
⇒
k
=
9
2
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