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MHT CET202310 May 2023Evening ShiftMathematicsVector AlgebraActual

The value of , so that the volume of parallelopiped formed by i + j + k , j + k and i + k becomes minimum, is

Options

  1. A-3
  2. B3
  3. C1 3
  4. D- 1 3

Correct answer

C. 1 3

Step-by-step solution

Volume of parallelopiped = | array ccc 1 & & 1 0 & 1 & & 0 & 1 array | V =1+ ^3- For maxima or minima, aligned & dV d =0 & 3 ^2-1=0 & = 1 3 aligned Now, d ^2 ~V ~d ^2 =6 For = 1 3 , d ^2 ~V ~d x^2 >0 V is minimum at = 1 3 .

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