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Let for a triangle A B C A B → = - 2 i ^ + j ^ + 3 k ^ C B → = α i ^ + β j ^ + γ k ^ C A → = 4 i ^ + 3 j ^ + δ k ^ If δ > 0 and the area of the triangle A B C is 5 6 then C B → · C A → is equal to

Options

  1. A60
  2. B54
  3. C108
  4. D120

Correct answer

A. 60

Step-by-step solution

Given, A triangle A B C A B → = - 2 i ^ + j ^ + 3 k ^ C B → = α i ^ + β j ^ + γ k ^ C A → = 4 i ^ + 3 j ^ + δ k ^ Now plotting the diagram we get, Now from triangle law of addition we get, C A → + A B → = C B → ⇒ 4 i ^ + 3 j ^ + δ k ^ + - 2 i ^ + j ^ + 3 k ^ = α i ^ + β j ^ + γ k ^ ⇒ 2 i ^ + 4 j ^ + δ + 3 k ^ = α i ^ + β j ^ + γ k ^ Now on comparing both side we get, α = 2 ,   β = 4   &#38

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