Three Dimensional Geometry · Question 5

Let R be such that the lines L1: x+111= y+212= z+293 and L2: x+163= y+112= z+4 intersect. Let R1 be the point of intersection of L1 and L2. Let O=(0,0,0), and n denote a unit normal vector to the plane containing both the lines L1 and L2. Match each entry in List-I to the correct entry in List-II.

1. (P) → (3) (Q) → (4) (R) → (1) (S) → (2)
2. (P) → (5) (Q) → (4) (R) → (1) (S) → (2)
3. (P) → (3) (Q) → (4) (R) → (1) (S) → (5)
4. (P) → (3) (Q) → (1) (R) → (4) (S) → (5)

Answer

(3) (P) → (3) (Q) → (4) (R) → (1) (S) → (5)

Solution

L1: (t-11, 2t-21, 3t-29); L2: (3s-16, 2s-11, s-4)

x: t=3s-5; y: t=s+5 s=5, t=10

R1=(-1,-1,1); z: 1=5 -4 =1

Normal: (1,2,3) (3,2,1)=(-4,8,-4) (1,-2,1) n= 1 6( i-2 j+ k)

OR1 n= -1+2+1 6= 2 6= 23

P → 3, Q → 4, R → 1, S → 5

Answer: (C)