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JEE Main202225 Jul 2022Morning ShiftMathematicsVector AlgebraActual

Let A B C be a triangle such that B C → = a → , C A → = b → , A B → = c → , a → = 6 2 , b → = 2 3 and b → · c → = 12 Consider the statements : S 1 : a → × b → + c → × b → - c → = 6 2 2 - 1 S 2 : ∠ A B C = cos - 1 2 3 . Then

Options

  1. Aboth S 1 and S 2 are true
  2. Bonly S 1 is true
  3. Conly S 2 is true
  4. Dboth S 1 and S 2 are false

Correct answer

C. only S 2 is true

Step-by-step solution

We know that by triangle law of vector addition, a → + b → + c → = 0 ⇒ b → + c → = - a → Squaring both side we get, b → 2 + c → 2 + 2 b → · c → = a → 2 Now putting the given value a → = 6 2 ,   b → = 2 3   &   b → . c → = 12 We get, c → 2 = 36 So, c → = 6 Now, S 1 :   a → × b → + c → × b → - c → ⇒ a → + c → × b →

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