Let a → , b → and c → be three non-zero vectors such that b → and c → are non-collinear if a → + 5 b → is collinear with c → , b → + 6 c → is collinear with a → and a → + α b → + β c → = 0 → , then α + β is equal to

Step-by-step solution

Given: a → + 5 b → is collinear with c → , b → + 6 c → is collinear with a → and a → + α b → + β c → = 0 → . ⇒ a → + 5 b → = λ c → . . . i ⇒ b → + 6 c → = μ a → . . . ii ⇒ a → = λ c → - 5 b → = b → + 6 c → μ ⇒ λ c → - 5 b → = 6 μ c → + 1 μ b → Comparing both the sides, ⇒ μ = - 1 5 , λ = - 30 Putting these values in equation i ⇒ a → + 5 b → = - 30 c → ⇒ a → + 5 b → + 30 c → = 0 Comparing this equation with a → + α b → + β c → = 0 → . ⇒ α = 5 , β = 30 ⇒ α + β = 35