Question

Match the following Columns:

Let P(0, 3, –2), Q(3, 7, –1) and R(1, –3, –1) be three given points. Let L₁ be the line passing through P and Q and L₂ be the line through R and parallel to the vector v = i + k.

	Column I		Column II
(A)	The perpendicular distance of P from L2 is	(P)	7√3
(B)	The shortest distance between L1 and L2 is	(Q)	6
(C)	Area of the ΔPQR is	(R)	√38
(D)	The distance from (0, 0, 0) to the plane PQR is	(S)	19/√147

Answer 1

Answer is 

(A) - (R) √38

(B) - (Q) 6

(C) - (P) 7√3

(D) - (S) 19/√147

Given

The equation of the plane PQR is

(A) Let the foot of the perpendicular on L₂ is M.

Thus, M = (λ + 1, –3, λ – 1)

The direction ratios of PM are (λ + 1, –6, λ + 1)

Since PM is perpendicular to L₂, so

1(λ + 1) + 0 + 1(λ + 1) = 0 

λ = – 2

Hence, the foot of the perpendicular is (–1, – 3, –3)

Thus, the length of the perpendicular = √(1 + 36 + 1)= √38 

(B) The shortest distance between L₁ and L₂

(C) Area of ΔPQR

(D) Hence, the distance from the origin to the plane 5x – y – 11z = 19