Let a → = 1 , b → = 4 and a → × r → + b → = r → . If the projection of r → along a → is 2 , then the projection of r → along b → is

Step-by-step solution

a → = 1 , b → = 4 , r → ⋅ a ^ = 2 a → × r → + b ^ = r → Taking dot with a → 0 + b → ⋅ a → = r → ⋅ a → b → ⋅ a → a → = r → ⋅ a → a → = 2 ⇒ a → ⋅ b → = 2 ...(i) ⇒ a → b → cos ⁡ θ = 2 ⇒ cos ⁡ θ = 1 2 ⇒ θ = 60 o (angle between a → and b → ) Taking dot with b → a → × r → ⋅ b → + b → ⋅ b → = r → ⋅ b → - r → a → b → + 16 = r → ⋅ b → ...(ii) Taking dot with a → × b → a → × r → ⋅ a → × b → + 0 = r → a → b → a → ⋅ a → a → ⋅ b → r → ⋅ a → r → ⋅ b → = 16 - r → ⋅ b → (using (ii)) 1 r → ⋅ b → - 2 × 2 = 16 - r → ⋅ b → (using (i))