1. Find Coplanar vectors
`A=(1,2,3)`, `B=(4,5,6)`, `C=(7,8,9)`

Solution:
Here `vec A=(1,2,3),vec B=(4,5,6),vec C=(7,8,9)`

The 3 vectors are coplanar, if their scalar triple product is zero
1. Calculate scalar triple product
`vec A*(vec B xx vec C)`

`=|[A_1,A_2,A_3],[B_1,B_2,B_3],[C_1,C_2,C_3]|`

=	`1`   `2`   `3`   `4`   `5`   `6`   `7`   `8`   `9`

=

`1`   `xx`    `5`   `6`   `8`   `9`

`-2`   `xx`    `4`   `6`   `7`   `9`

`+3`   `xx`    `4`   `5`   `7`   `8`

`=1 xx (5 xx 9 - 6 xx 8) -2 xx (4 xx 9 - 6 xx 7) +3 xx (4 xx 8 - 5 xx 7)`

`=1 xx (45 -48) -2 xx (36 -42) +3 xx (32 -35)`

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

`= -3 +12 -9`

`=0`


Here scalar triple product is zero, so vectors are coplanar

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2. Find Coplanar 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)`

The 3 vectors are coplanar, if their scalar triple product is zero
1. Calculate scalar triple product
`vec A*(vec B xx vec C)`

`=|[A_1,A_2,A_3],[B_1,B_2,B_3],[C_1,C_2,C_3]|`

=	`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`

`!=0`

Here scalar triple product is not zero, so vectors are not coplanar

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