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Q.

Let l1 and l2 be the lines r1=λ(i^+j^+k^) and r2=(j^k^)+μ(i^+k^), respectively, Let X be the set of all the planes H that contain the line l1. For a plane H, let d(H) denote the smallest possible distance between the points of l2 and H. Let H0 be a plane in X for which d(H0) 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(H0) is1)3
Q)The distance of the point (0, 1, 2) from H0 is2)13
R)The distance of origin from H0 is3)0
S)The distance of origin from the point of intersection of planes y = z, x = 1 and H0 is4)2
  5)12
 PQRS
1)2451
2)5431
3)2132
4)5142

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a

2

b

1

c

3

d

4

answer is B.

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Detailed Solution

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1:r1=λ(i+j+k)=a¯+λb¯ 2:r2¯=jk+μ(i+k)=c¯+μd¯
Here, a¯c¯    b¯    d¯=011111101=10
l1 and l2 are skew lines.
 H0 is the plane containing l1 and parallel to l2
Equation of H0 is x    y    z1    1    11    0    1=0xz=0
P) d(Ho) = Shortest distance between l1 and l212
Q) d=022=2
R) Ho passes through (0, 0, 0)
S) Point of intersection of given planes and Ho is (1, 1, 1) 
Distance from origin =(10)2+(10)2+(10)2=3
P5,Q4,R3,S1

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Let l1 and l2 be the lines r→1=λ(i^+j^+k^) and r→2=(j^−k^)+μ(i^+k^), respectively, Let X be the set of all the planes H that contain the line l1. For a plane H, let d(H) denote the smallest possible distance between the points of l2 and H. Let H0 be a plane in X for which d(H0) 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(H0) is1)3Q)The distance of the point (0, 1, 2) from H0 is2)13R)The distance of origin from H0 is3)0S)The distance of origin from the point of intersection of planes y = z, x = 1 and H0 is4)2  5)12 PQRS1)24512)54313)21324)5142