Question

Find the volume of the tetrahedron whose vertices are (1, 2, 1), (3, 2, 5), (2, -1, 0) and (-1, 0, 1).

Answer 1

Answer:

                   The Volume of Tetrahedron = 6 cubic units

Step-by-step explanation:

The given points are

A(1, 2, 1), B(3, 2, 5), C(2, -1, 0) and D(-1, 0, 1)

Then

u = AB = ( 3 -1 , 2 - 2 , 5 - 1 ) = ( 2 , 0 , 4 )

v = AC = ( 2 -1 , -1 - 2 , 0 - 1 ) = ( 1 , - 3 , - 1)

w = AD = ( -1 - 1 , 0 - 2 , 1 - 1 ) = ( - 2 , - 2 , 0 )

Now

Volume of Tetrahedron = 1/6 [ u v w ]

So we have

    [ u v w ]

$=\left[\begin{array}{ccc}2&0&4\\1&-3&-1\\-2&-2&0\end{array}\right] \\\\=2(0-2)-0+4(-2-6)\\=-4+4(-8)\\=-4-32\\=-36\\So\\VolemeOfTetrahedron=\frac{1}{6}(-36)=-6=6\\ BecauseVolumeIsPositive$

The Volume of Tetrahedron = 6 cubic units

Answer 2

Answer:

please see the above attachment....