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📐 Mathematics  ·  Vector Algebra  ·  JEE

The volume of the tetrahedron with one vertex at origin, others at a, b, c is:

Answer: (1/6)|[a b c]|.

  • A |[a b c]|
  • B (1/3)|[a b c]|
  • C (1/2)|[a b c]|
  • D (1/6)|[a b c]|

Correct answer: D. (1/6)|[a b c]|

Explanation: Volume of tetrahedron = (1/6)|a.(b x c)|. The parallelepiped formed by the same edges has volume |[abc]|, and the tetrahedron is 1/6 of that.

xya (4,1)b (2,3)a + b (6,4)

Triangle law of vector addition: placing vector b at the head of vector a, the diagonal from the start to the final head gives the resultant a + b.

Concept context

Vectors, dot product, cross product, and geometric applications

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