The magnitude of x and y components of A → are 7 and 6 respectively. Also, the magnitudes of x and y components of A → + B → are 11 and 9 respectively. Calculate the magnitude of vector B → .

Step-by-step solution

Given, A → = 7 i ^ + 6 j ^ Let B → = b 1 i ^ + b 2 j ^ ......(i) Given that, A → + B → = 11 i ^ + 9 j ^ Or 7 + b 1 i ^ + 6 + b 2 j ^ = 11 i ^ + 9 j ^ Comparing the scalar component of i ^ and j ^ 7 + b 1 = 11 and 6 + b 2 = 9 ⇒ b 1 = 4 and b 2 = 3 ∴ From Equation. (i), B → = 4 i ^ + 3 j ^ B → = 4 2 + 3 2 = 25 = 5