Question

The acute angle between the planes P₁ and P₂ , when P₁ and P₂ are the planes passing through the intersection of the planes 5x + 8y + 13z – 29 = 0 and 8x – 7y + z – 20 = 0 and the points (2, 1, 3) and (0, 1, 2), respectively, is

(A) π/3 

(B) π/4

(C) π/6

(D) π/12

Answer 1

Correct option is (A) π/3 

Equation of plane passing through the intersection of planes 

5x + 8y + 13z –29 = 0 and 8x – 7y + z – 20 = 0 is

5x + 8y + 3z - 29 + λ(8x - 7y + z - 20) = 0 and

if it is passing through (2,1,3) then λ = 7/2

P₁: Equation of plane through intersection of

5x + 8y + 13z - 29 = 0 and 8x - 7y + z - 20 = 0 and the point (2, 1, 3) is

5x + 8y + 3z - 29 + 7/2 (8x  -7y + z - 20) = 0

⇒ 2x - y + z = 6

Similarly P₂ : Equation of plane through 2 intersection of

5x + 8y + 13z - 29 = 0 and 8x - 7y + z - 20 = 0 and the point (0,1,2) is

⇒ x + y + 2z = 5

Angle between planes = θ = cos^-1 (3/√6 √6) = π/3