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`

Explanation

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`

...