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

Solution:
Here `vec A=(1,2,3),vec B=(2,4,6),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]|`

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

=

`1`   `xx`    `4`   `6`   `4`   `5`

`-2`   `xx`    `2`   `6`   `3`   `5`

`+3`   `xx`    `2`   `4`   `3`   `4`

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

`=1 xx (20 -24) -2 xx (10 -18) +3 xx (8 -12)`

`=1 xx (-4) -2 xx (-8) +3 xx (-4)`

`= -4 +16 -12`

`=0`


Here scalar triple product is zero, so vectors are coplanar

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2. Find Coplanar 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)`

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`   `-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`

`!=0`

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

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