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MHT CET202519 Apr 2025Morning ShiftMathematicsVector AlgebraActual

The volume of the tetrahedron whose co-terminus edges are a , ~b , c is 12 cubic units. If the scalar projection of a on b c is 4 , then | b c |=

Options

  1. A18
  2. B1 18
  3. C16
  4. D1 16

Correct answer

A. 18

Step-by-step solution

The volume of a tetrahedron with coterminous edges a , b , and c is given by V = 1 6 | a ( b c )| . Given V = 12 yields | a ( b c )| = 72 . The scalar projection of a on b c is a ( b c ) | b c | = 4 , so a ( b c ) = 4 | b c | . Substituting into the volume expression gives 4 | b c | = 72 , hence | b c | = 18 . Answer: 18

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