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Prove that a necessary and sufficient...

Prove that a necessary and sufficient condition for three vectors ` vec a , vec b` and ` vec c` to be coplanar is that there exist scalars `l , m , n` not all zero simultaneously such that `l vec a+m vec b+n vec c= vec0dot`

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Verified by Experts

Here, it is given that ,
`lveca+mvecb+nvecc = 0`
If we put, `l =-1 , m = x and n = y`, then,
`-veca +xvecb+yvecc = 0`
`=> veca = xvecb+yvecc`, which is the neccessary condition for all three vectors to be coplanar.
Now,
`lveca+mvecb+nvecc = 0`
...
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