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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The length of two opposite edges of a tetrahedron are 12 and 15 units and the shortest distance between them is 10 units. If the volume of the tetrahedron is 200 cubic units, then the angle between the 2 edges is

Options

  1. As i n - 1 1 2
  2. Bs i n - 1 2 3
  3. Cs i n - 1 3 4
  4. Ds i n - 1 4 5

Correct answer

B. s i n - 1 2 3

Step-by-step solution

Let, A B C D be the tetrahedron and position vectors of A , B , C , D be a → , b → , c → , d → respectively. Given, b → - a → = 12 & d → - c → = 15 Shortest distance = d → - b → ⋅ b → - a → × d → - c → b → - a → × d → - c → = 10 ... 1 Also, volume = 1 6 d → - a → ⋅ b → - a → × c → - a → = 200 ... 2 From 1 and 2 , we get, b → - a → × d → - c → × 10 = 6 × 200 b → - a → d → - c → sin ⁡ θ = 120 sin ⁡ θ = 2 3 ⇒ θ = s i n - 1 2 3

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