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MHT CET20242 May 2024Morning ShiftMathematicsVector AlgebraActual

The volume of parallelopiped formed by vectors i +m j + k , j +m k and m i + k becomes minimum when m is

Options

  1. A2
  2. B3
  3. C3
  4. D1 3

Correct answer

D. 1 3

Step-by-step solution

Volume of the parallelopiped formed by vectors is i.e., V= | array ccc 1 & m & 1 0 & 1 & m m & 0 & 1 array |=1-m+m^3 d V d m =-1+3 m^2, d^2 V d a^2 =6 m For max. or . of V, d V d m =0 m ^2= 1 3 m = 1 3 d^2 V d m^2 =6 m 0 for m= 1 3 V is minimum for m = 1 3

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