If `a ,\ b ,\ c` are non coplanar vectors prove that the points having the following position vectors are collinear: ` vec a+ vec b+ vec c ,\ 4 vec a+3 vec b ,\ 10 vec a+7 vec b-2 vec c cdot`

Explanation

Given: `vec(a), vec(b), vec(c)` are non-coplanar vectors.


Let the points be with the position vectors


`A= vec(a)+vec(b)+vec(c)`


`B=4 vec(a)+3 vec(b)`


`C= 10 vec(a)+7 vec(b)-2 vec(c)`


Then `vec(A B)=` Position vector of `B-` Position vector of `A`


`=4 vec(a)+3 vec(b)-vec(a)-vec(b)-vec(c)`


`rArr vec(AB)=3 vec(a)+2 vec(b)-vec(c)`


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