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Question
Mathematics
If the lines (2x-1/2)=(3-y/1)=(z-1/3)and (x+3/2)=(z+1/p)=(y+2/5) are perpendicular to each other, then p is equal to
Q. If the lines
2
2
x
−
1
=
1
3
−
y
=
3
z
−
1
an
d
2
x
+
3
=
p
z
+
1
=
5
y
+
2
are perpendicular to each other, then
p
is equal to
3060
206
KEAM
KEAM 2013
Three Dimensional Geometry
Report Error
A
1
B
−
1
C
10
D
−
5
7
E
−
19
Solution:
Given lines are
2
2
x
−
1
=
1
3
−
y
=
3
z
−
1
⇒
1
x
−
1/2
=
−
1
y
−
3
=
3
z
−
1
…
(
i
)
and
2
x
+
3
=
p
z
+
1
=
5
y
+
2
…
(
ii
)
Since, both lines are perpendicular.
∴
(
1
)
(
2
)
+
(
−
1
)
(
5
)
+
(
3
)
(
p
)
=
0
(by perpendicularity condition)
⇒
2
−
5
+
3
p
=
0
⇒
3
p
=
3
∴
p
=
1