Let y=mx+λi,i=1,2,3,...,n be a family of n parallel lines subjected to following conditions. (1) m being a constant (2) n∑i=1λi=1 A variable line through origin intersects the lines at Pi(i=1,2,3,...,n) and Q be a point on variable line such that n∑i=1OPi=OQ. If the locus of Q is a straight line which passes through a fixed point (a,b) ∀ m∈R, then the value of (3a+2b) is

Let y=mx+λi,i=1,2,3,...,n be a family of n parallel lines subjected

1.	Let y=mx+λi,i=1,2,3,...,n be a family of n parallel lines subjected to following conditions. (1) m being a constant (2) n∑i=1λi=1 A variable line through origin intersects the lines at Pi(i=1,2,3,...,n) and Q be a point on variable line such that n∑i=1OPi=OQ. If the locus of Q is a straight line which passes through a fixed point (a,b) ∀ m∈R, then the value of (3a+2b) is
Answer» Let $y = m x + λ_{i}, i = 1, 2, 3, . . ., n$ be a family of $n$ parallel lines subjected to following conditions. $(1) m$ being a constant $(2) n \sum i = 1 λ_{i} = 1$ A variable line through origin intersects the lines at $P_{i} (i = 1, 2, 3, . . ., n)$ and $Q$ be a point on variable line such that $n \sum i = 1 O P_{i} = O Q$ . If the locus of $Q$ is a straight line which passes through a fixed point $(a, b) \forall m \in R,$ then the value of $(3 a + 2 b)$ is