Question: Let <img src="https://cdn.pureessence.tech/canvas_283.png?top_left_x=1117&top_left_y=1460&width=300&...

Question

Let be two unit vectors such that $\hat { a } + \hat { b }$ is also a unit vector. Then the angle betweenis

Answer 1

Since $\hat { a } + \hat { b }$ is a unit vector, ( $\hat { a } + \hat { b }$ ).( $\hat { a } + \hat { b }$ ) =1

⇒ + + 2 $\hat { a } \cdot \hat { b }$ =1 ⇒ 1 +1 + 2 $\hat { a } \cdot \hat { b }$ =1

⇒ $\hat { a } \cdot \hat { b }$ = -1/2.

Hence the angle θ between $\hat { a ̂ }$ and $\hat { b }$ is given by

cosθ = -1/2 ⇒ θ =120⁰