The magnitude of vectors OA → , OB → and OC → in the given figure are equal. The direction of OA → + OB → - OC → with x - axis will be:

Step-by-step solution

From the above diagram, the equations are, OA → = R cos 30 ∘ i ^ + sin 30 ∘ j ^ OB → = R cos 60 ∘ i ^ - sin 60 ° j ^ OC → = R - cos 45 ° i ^ + sin 45 ° j ^ ⇒ OA → + OB → − OC → = R 1 2 + 3 2 + 1 2 i ^ + R 1 2 − 3 2 − 1 2 j ^ , angle with the x - axis. ⇒ tan α = 1 2 − 3 2 − 1 2 1 2 + 3 2 + 1 2 = 1 − 3 − 2 1 + 3 + 2 ⇒ α = tan − 1 1 − 3 − 2 1 + 3 + 2 .