1. Find Volume of Parallelepiped determined by vectors
`A=(1,2,3)`, `B=(3,0,6)`, `C=(7,1,9)`

Solution:
Here `vec A=(1,2,3),vec B=(3,0,6),vec C=(7,1,9)`

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

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

=	`1`   `2`   `3`   `3`   `0`   `6`   `7`   `1`   `9`

=

`1`   `xx`    `0`   `6`   `1`   `9`

`-2`   `xx`    `3`   `6`   `7`   `9`

`+3`   `xx`    `3`   `0`   `7`   `1`

`=1 xx (0 xx 9 - 6 xx 1) -2 xx (3 xx 9 - 6 xx 7) +3 xx (3 xx 1 - 0 xx 7)`

`=1 xx (0 -6) -2 xx (27 -42) +3 xx (3 +0)`

`=1 xx (-6) -2 xx (-15) +3 xx (3)`

`= -6 +30 +9`

`=33`


2. Calculate parallelepiped volume
Volume `=33`

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

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

=

`5`   `xx`    `3`   `4`   `4`   `5`

`+1`   `xx`    `-2`   `4`   `3`   `5`

`+1`   `xx`    `-2`   `3`   `3`   `4`

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

`=5 xx (15 -16) +1 xx (-10 -12) +1 xx (-8 -9)`

`=5 xx (-1) +1 xx (-22) +1 xx (-17)`

`= -5 -22 -17`

`=-44`


2. Calculate parallelepiped volume
Volume `=44`

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