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MHT CET202526 Apr 2025Morning ShiftMathematicsVector AlgebraActual

The volume of tetrahedron with co-terminus edges a , ~b , c is 64 3 cubic units, then volume of parallelopiped considering coterminus edges given by the vectors a + b , b + c , c + a is ... cubic units.

Options

  1. A384
  2. B128 3
  3. C256
  4. D32 3

Correct answer

C. 256

Step-by-step solution

Volume calculation for tetrahedron and parallelepiped Given three coterminous edges a , b , and c of a tetrahedron with volume 64 3 , the scalar triple product magnitude is |[ a b c ]| = 6 64 3 = 128 . For the parallelepiped with edges a + b , b + c , and c + a , the scalar triple product satisfies [ a + b b + c c + a ] = 2[ a b c ] . The volume is therefore |2[ a b c ]| = 2 128 = 256 . The volume of the parallelepiped is 256 .

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