See image — AITS & Test Series Chemistry Question

💡 Solution & Explanation

(I) Let A(a, 0, 0), B(0, b, 0) and C(0, 0, c) then a = 1, b = 2, c = 3 and equation of plane is x y z 1 1 2 3    (II) Let the plane is (x + y + 2z – 7) +  (2x – y + z – 6) = 0 and (1 + 2). 2 + (1 - ). 3 + (2 + ). 1 = 0  plane is 12x – 99y + 3z – 28 = 0 (III) Required plane is x 3 y 1 z 2 2 3 1 0 x y z 0 3 1 2           (IV) Let plane is a(x 1) b(y 1) c(z 2) 0       since this is parallel to given lines 2a 3b 4c 0,a 2b c 0       now on eliminating a, b, c we get 5x 2y z 5    .