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Find the Volume of a Tetrahedron Whose Vertices Are A(−1, 2, 3), B(3, −2, 1), C(2, 1, 3) and D(−1, −2, 4) - Mathematics and Statistics

Find the volume of a tetrahedron whose vertices are A(−1, 2, 3), B(3, −2, 1), C(2, 1, 3) and D(−1, −2, 4).

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Solution

Let `bara , barb , barc , bard` be the position vectors of points A, B, C, D respectively of a
tetrahedron.

= `1/6 [4(-1-0) + 4(3 - 0) - 2(-12 - 0)]`

= 1/6 (-4+12 + 24)

= 1/6 (32)

= `16/3`

∴ Volume of the tetrahedron is `16/3` cubic units

 

Concept: Vectors - Collinearity and Coplanarity of Vectors
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