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JEE Advanced 2018 Paper 1
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© examsnet.com
Question : 39
Total: 54
Let
P
1
:
2
x
+
y
−
z
=
3
and
P
2
:
x
+
2
y
+
z
=
2
be two planes.Then which of the following statements (s) is are TRUE ?
The line of intersection of
P
1
and
P
2
has direction ratios
1
,
2
,
−
1
The line
3
x
−
4
9
=
1
−
3
y
9
=
z
3
is perpendicular to the line of intersection of
P
1
and
P
2
The acute angle between
P
1
and
P
2
is 60°
If
P
3
is the plane passing through the point
(
4
,
2
,
−
2
)
and perpendicular to the lineof intersection of
P
1
and
P
2
,then the distance of the point
(
2
,
1
,
1
)
from the plane
P
3
is
2
√
3
Validate
Solution:
D.C of the line of intersection
(
a
,
b
,
c
)
⇒
2
a
+
b
−
c
=
0
a
+
2
b
+
c
=
0
a
1
+
2
=
b
−
1
−
2
=
c
4
−
1
∴ DC is
(
1
,
−
1
,
1
)
3
x
−
4
9
=
1
−
3
y
9
=
z
3
⇒
x
−
4
/
3
3
=
y
−
1
/
3
−
3
=
z
3
⇒lines are parallel
Acute angle between
P
1
and
P
2
=
c
o
s
−
1
(
2
×
1
+
1
×
2
−
1
×
1
√
6
√
6
)
=
c
o
s
−
1
(
3
6
)
=
c
o
s
−
1
(
1
2
)
=
60
°
Plane is given by
(
x
−
4
)
−
(
y
−
2
)
+
(
z
+
2
)
=
0
⇒
x
−
y
+
z
=
0
Distance of
(
2
,
1
,
1
)
from plane
=
2
−
1
+
1
√
3
=
2
√
3
© examsnet.com
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