Which of the following relations is true for two unit vector A ^ and B ^ making an angle θ to each other?

Step-by-step solution

We know, 1 -   cos   θ = 2 sin 2 θ 2 1 +   cos   θ = 2 cos 2 θ 2 Now, a → + b → · a → + b → = a → 2 + 2 a → · b → + b → 2 ⇒ a → + b → · a → + b → = 1 2 + 2 × 1 × 1 × cos θ + 1 2   ⇒ a → + b → · a → + b → = 2 1 + cos θ ⇒ a → + b → 2 = 4 cos 2 θ 2 ⇒ a → + b → = 2 cos θ 2