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AP EAMCET20226 Jul 2022Evening ShiftMathematicsVector AlgebraActual

Let P be a real number and |P| 2 . If A, B, C are variable angles such that ( P^2-4 ) A+P B+ ( P^2+4 ) C=6 P , then the minimum value of ^2 A+ ^2 B+ ^2 C=

Options

  1. A6
  2. B8
  3. C12
  4. D18

Correct answer

C. 12

Step-by-step solution

Let a = P^2-4 i +P j + P^2+4 k and b = A i + B j + C k are two vector expression a b = P^2-4 A+P B+ P^2+4 C| a || b | =6 P , where Q is the angle between a and b aligned & P^2-4+P^2+P^2+4 ^2 A+ ^2 B+ ^2 C & =6 P aligned aligned & =6 P & 3 P ^2 A+ ^2 B+ ^2 C =6 P aligned Squaring both sides, aligned & Squaring both sides, & 3 [ ^2 A+ ^2 B+ ^2 C ]=36 ^2 aligned ^2 A+ ^2 B+ ^2 C=12 ^2 As we know that ^2 1,12 ^2 12 ^2 A+ ^2 B+ ^2 C 12 Minimum value of ^2 A+ ^2 B+ ^2 C=12

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