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Byju's Answer
Standard XII
Mathematics
Global Maxima
Prove that th...
Question
Prove that the lines
[
x
+
3
3
=
y
+
3
5
=
z
+
5
7
]
&
[
x
+
2
1
=
y
−
4
3
=
z
−
6
5
]
not intersect at the point
[
1
2
,
−
1
2
,
−
3
2
]
?
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Solution
Lines are as
x
+
3
3
=
y
+
3
5
=
z
+
5
7
=
λ
1
x
+
2
1
=
y
−
4
3
=
z
−
6
5
=
λ
2
From equation (i) we can write .
x
1
=
3
λ
1
−
3
;
y
1
=
5
λ
1
−
3
;
z
1
=
7
λ
1
−
5
From equation (ii) we can write
x
1
=
λ
2
−
2
;
y
1
=
3
λ
2
+
4
;
z
1
=
5
λ
2
+
6
So,
x
1
=
3
λ
1
−
3
=
λ
2
−
2
3
λ
1
−
λ
2
=
1
...(iii)
Similarly,
y
1
=
6
λ
1
−
3
=
3
λ
2
+
4
5
λ
1
−
3
λ
2
=
7
...(iv)
λ
2
=
3
λ
1
−
1
substitute in equation ......(iv)
⇒
5
λ
1
−
3
(
3
λ
1
−
1
)
=
7
⇒
5
λ
1
−
9
λ
1
+
3
=
7
⇒
−
4
λ
1
=
4
⇒
λ
1
=
−
1
λ
2
=
3
λ
1
−
1
=
3
(
−
1
)
−
1
=
−
4
⇒
−
4
⇒
λ
2
=
−
4
Now if we check
z
1
=
7
λ
1
−
5
=
5
λ
2
+
6
7
(
−
1
)
−
5
=
5
(
−
4
)
+
6
−
12
=
−
14
not possible
So, Both lines will not interset each other
Suggest Corrections
0
Similar questions
Q.
Prove that the lines
x
+
1
3
=
y
+
3
5
=
z
+
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7
and
x
−
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=
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Q.
Show that the lines
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and
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Q.
The point of intersection of the lines
x
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a
n
d
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is
Q.
Show that the lines:
x
+
1
3
=
y
+
3
5
=
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+
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and
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intersect each other. Find the co-ordinates of intersecting point also.
Q.
On which of the following lines lies the point of intersection of the line,
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−
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x
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