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