Let 
and 
be the lines 
and 
, respectively. Let X be the set of all the planes H that contain the line 
. For a plane H, let d(H) denote the smallest possible distance between the points of 
and H. Let H 0 be plane in X for which d(H 0 ) is the maximum value of d(H) as H varies over all planes in X.
Match each entry in List-I to the correct entries in List-II.
List-I List-II
(P) The value of d(H 0 ) is (1) 
(Q) The distance of the point (0,1,2)
from H 0 is (2) 
(R) The distance of origin from H 0 is (3) 0
(S) The distance of origin from the
point of intersection (4) 
of planes y = z, x = 1 and H 0 is
The correct option is :
(2) (Q) 
(4) (R) 
(5) (S) 
(1)
(5) (Q) 
(4) (R) 
(3(S) 
(1)
(2) (Q) 
(1) (R) 
(3) (S) 
(2)
(5) (Q) 
(1) (R) 
(4) (S) 
(2)
Text Solution
Verified by ExpertsB
Let system of planes are
ax + by + cz = 0 ----(1)
It contain L 1
a + b + c = 0 …..(2)
For largest possible distance between plane (1) and L 2 the line L 2 must be parallel to plane (1)
a + c = 0 ....(3)
Plane H 0 : x-z = 0
Now d(H 0 ) = 
distance from point (0, 1, -1) on L 2 to plane.
for 'Q' distance 
(0, 0, 0) lies on plane
R 
3
For 'S' x = z ; y = z ; x = 1
point of intersection p(l, 1, 1).
option [b] is correct
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