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Let Δ P Q R be a triangle. Let a → = Q R → , b → = R P → a n d c → = P Q → . If a → = 12 , b → = 4 3 and b → ⋅ c → = 24 , then which of the following is (are) true ?

Options

  1. Ac → 2 2 - a → = 12
  2. Bc → 2 2 - a → = 30
  3. Ca → × b → + c → × a → = 48 3
  4. Da → ⋅ b → = - 72

Correct answer

A. c → 2 2 - a → = 12

Step-by-step solution

a → = 12 , b → = 4 3 , b . → c → = 24 a → + b → + c → = 0 (Sides of triangle) b → + c → = - a → b → + c → . b → + c → = - a → . - a → b → 2 + c → 2 + 2 b → . c → = a → 2 48 + c → 2 + 2 × 24 = 12 2 c → 2 = 48 c → 2 2 - a → = 48 2 - 12 = 12 c → 2 2 + a → = 48 2 + 12 = 36 a → × b → + c → × a → = a → × b → - a → × c → = a → × b → - c → a → = - b → - c → = - b → - c → × b → - c → = b → - c → × b → + c → = 2 b → × c → = 2 b → 2 c → 2 - b → . c → 2 = 2 48 × 48 - 24 2 = 2 × 24 4 - 1 = 48 3 a → + b → = - c → a → + b → . a →

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