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The value of a , such that the volume of the parallelopiped formed by the vectors i ^ + j ^ + k ^ , j ^ + a k ^ and a i ^ + k ^ becomes minimum, is

Options

  1. A3
  2. B- 1 3
  3. C1 2
  4. D- 2

Correct answer

C. 1 2

Step-by-step solution

Volume of parallelopiped = a → b → c → Here, the parallelopiped is formed by the vectors i ^ + j ^ + k ^ , j ^ + a k ^ and a i ^ + k ^ So, the volume, V = 1 1 1 0 1 a a 0 1 = 1 + a 2 - a = 3 4 + a - 1 2 2 cubic units Hence, the volume of the parallelopiped is minimum when a = 1 2

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