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MHT CET20244 May 2024Morning ShiftMathematicsVector AlgebraActual

The value of a for which the volume of parallelepiped formed by i +a j + k , j +a k and a i + k becomes minimum is

Options

  1. A-1 3
  2. B1 3
  3. C3
  4. D- 3

Correct answer

B. 1 3

Step-by-step solution

i.e., V= | array lll 1 & a & 1 0 & 1 & a a & 0 & 1 array | 1-a+a^3 d V d a =-1+3 a^2, d^2 V d a^2 =6 a For max. or min. of V, d V d a =0 a ^2= 1 3 a= 1 3 . d^2 V d a^2 =6 a 0 for a= 1 3 V is minimum for a = 1 3

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