The points with position vectors `overset(to)(a)+overset(to)(b),overset(to)(a)-overset(to)(b)` and `overset(to)(a)+koverset(to)(b)` are collinear for all real values of k.

The points with position vectors `overset(to)(a)+overset(to)(b),overse

1.	The points with position vectors `overset(to)(a)+overset(to)(b),overset(to)(a)-overset(to)(b)` and `overset(to)(a)+koverset(to)(b)` are collinear for all real values of k.
Answer» Let position vectors of points `vec(A) ,vec(B) " and " vec(C )` be `vec(a)+ vec(b), vec(a) -vec(b) " and " vec(a)+ kvec(b)` respectively . `:. (vec(a)-vec(b)) -(vec(a)+vec(b)) =(vec(a)+kvec(b)) - (vec(a)- vec(b))` `rArr -2vec(b) =(k +1) vec(b)` `rArr k+1 =-2` `rArr k=-3` Hence it is false statement .

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The points with position vectors `overset(to)(a)+overset(to)(b),overset(to)(a)-overset(to)(b)` and `overset(to)(a)+koverset(to)(b)` are collinear for all real values of k.

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