1. Find Volume of Parallelepiped determined by vectors
`A=(5,6,1)`, `B=(0,2,3)`, `C=(3,4,5)`

Solution:
Here `vec A=(5,6,1),vec B=(0,2,3),vec C=(3,4,5)`

Volume `=|vec A * (vec B xx vec C)|`

1. Calculate scalar triple product
`vec A * (vec B xx vec C)`

=	`5`   `6`   `1`   `0`   `2`   `3`   `3`   `4`   `5`

=

`5`   `xx`    `2`   `3`   `4`   `5`

`-6`   `xx`    `0`   `3`   `3`   `5`

`+1`   `xx`    `0`   `2`   `3`   `4`

`=5 xx (2 xx 5 - 3 xx 4) -6 xx (0 xx 5 - 3 xx 3) +1 xx (0 xx 4 - 2 xx 3)`

`=5 xx (10 -12) -6 xx (0 -9) +1 xx (0 -6)`

`=5 xx (-2) -6 xx (-9) +1 xx (-6)`

`= -10 +54 -6`

`=38`


2. Calculate parallelepiped volume
Volume `=38`

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2. Find Volume of Parallelepiped determined by vectors
`A=(0,2,3)`, `B=(5,6,1)`, `C=(1,5,6)`

Solution:
Here `vec A=(0,2,3),vec B=(5,6,1),vec C=(1,5,6)`

Volume `=|vec A * (vec B xx vec C)|`

1. Calculate scalar triple product
`vec A * (vec B xx vec C)`

=	`0`   `2`   `3`   `5`   `6`   `1`   `1`   `5`   `6`

=

`0`   `xx`    `6`   `1`   `5`   `6`

`-2`   `xx`    `5`   `1`   `1`   `6`

`+3`   `xx`    `5`   `6`   `1`   `5`

`=0 xx (6 xx 6 - 1 xx 5) -2 xx (5 xx 6 - 1 xx 1) +3 xx (5 xx 5 - 6 xx 1)`

`=0 xx (36 -5) -2 xx (30 -1) +3 xx (25 -6)`

`=0 xx (31) -2 xx (29) +3 xx (19)`

`= 0 -58 +57`

`=-1`


2. Calculate parallelepiped volume
Volume `=1`

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