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The position vectors of the four angu...

The position vectors of the four angular points of a tetrahedron are `A( hat j+2 hat k),B(3 hat i+ hat k), C(4 hat i+3 hat j+6 hat k)a n dD(2 hat i+3 hat j+2 hat k)dot` Find the volume of the tetrahedron `A B C Ddot`

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Vertices of tetrahedron are `A(hatj+2hatk),B(3hati+hatk),C(4hati+3hatj+6hatk) and D(2hati+3hatj+2hatk)`.Threrfore,
`vec(AB)=3hati-hatj-hatk,vec(AC)=4hati+2hatj+4hatk and vec(AD)=2hati+2hatj`
volume, ` V=1/6[vec(AB)" " vec(AV)" "vec(AD)]`
`=1/6 |{:(3,-1,-1),(4,2,4),(2,2,0):}|`
2 cubic unit
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