The points with position vectors `veca + vecb, veca-vecb and veca +k vecb` are collinear for all real values of k.

Answer

True

Explanation

Let position vectors of points A, B and C be
`veca + vecb, veca - vecb and veca +kvecb`, respectively.
Then `vec(AB) = (veca - vecb ) - (veca + vecb) = -2 vecb`
Similarly, `vec(BC) = (veca + k vecb) - (veca - vecb) = (k+1)vecb`
Clearly `vec(AB) "||" vec(BC) AA k in R`
Hence, A, B and C are collinear `AA k inR`
Therefore, the statement is true.