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JEE Advanced 2018 Paper 2
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© examsnet.com
Question : 48
Total: 54
Let P be a point in the first octant, whose image Q in the plane
x
+
y
=
3
(that is, the line segment PQ is perpendicular to the plane
x
+
y
=
3
and the mid-point of PQ lies in the plane
x
+
y
=
3
) Lie on the z-axis. Let the distance of P from the x-axis be 5. If R is the image of P in the xy-plane, then the length of PR is_____
Your Answer:
Validate
Solution:
Let
P
(
α
,
β
,
γ
)
Q
(
0
,
0
,
γ
)
&
R
(
α
,
β
,
−
γ
)
Now
−
P
Q
|
|
⋀
i
+
⋀
j
⇒
(
α
⋀
i
+
β
⋀
j
)
|
|
(
⋀
i
+
⋀
j
)
⇒
α
=
β
Also, mid point of PQ lies on the plane
⇒
α
2
+
β
2
=
3
⇒
α
+
β
=
6
⇒
α
=
3
Now, distance of point P from X-axis
√
β
2
+
γ
2
=
5
⇒
β
2
+
γ
2
=
25
⇒
γ
2
=
16
as
β
=
α
=
3
as
γ
=
4
Hence
P
R
=
2
γ
=
8
© examsnet.com
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