If two points A and B lie on the curve y = x 2 such that O A → ⋅ i ^ = 1 and O B → ⋅ j ^ = 4 , where O is the origin and A and B lie in the 1 s t and 2 n d quadrant respectively, then O A → ⋅ O B → is equal to

Step-by-step solution

Let the points A , B be α , α 2 , β , β 2 respectively where α > 0 ,   β < 0 O A → = α i ^ + α 2 j ^ O B → = β i ^ + β 2 j ^ O A → ⋅ i ^ = α = 1 ⇒ O A → = i ^ + j ^ O B → ⋅ j ^ = β 2 = 4 ⇒ β = ± 2 ∵ β < 0 ⇒ β = - 2 ⇒ O B → = - 2 i ^ + 4 j ^ O A → ⋅ O B → = i ^ + j ^ - 2 i ^ + 4 j ^ = - 2 + 4 = 2