The vectors 3 a → - 5 b → and 2 a → + b → are mutually perpendicular and the vectors a → + 4 b → and - a → + b → are also mutually perpendicular. Then the angle between the vectors a → and b → , is

Step-by-step solution

∵ ( 3 a → - 5 b → ) ⋅ ( 2 a → + b → ) = 0 ∴ a → ⋅ b → = 6 a → 2 - 5 b → 2 7 ...(i) and ( a → + 4 b → ) ⋅ ( b → - a → ) = 0 ∴ a → ⋅ b → = 4 b → 2 - a → 2 3 ...(ii) ∴ From equation (i) and (ii), a → = 43 25 b → and a → ⋅ b → = a → b → cos ⁡ θ ∴ cos ⁡ θ = 19 b → 2 43 25 b → 2 = 19 5 43