If ` vec a , vec b` are two non-collinear vectors, prove that the points with position vectors ` vec a+ vec b , vec a- vec b` and ` vec a+lambda vec b` are collinear for all real values of `lambdadot`

Explanation

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


Let the points be with the position vectors


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


`B=vec(a)- vec(b)`


`C=vec(a)+lambda vec b`
are collinear.

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


`=(vec(a)- vec(b))-(vec(a)+vec(b))`


`rArr vec(AB)=-2 vec(b)`


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