Question Detail
Question
Two vectors A and B are given as follows: A = 3.0i - 4.5j and B = -2.5i + 5.0j. Find the magnitude of their vector sum and the angle it makes with the positive x-axis.
Correct Answer
Option B is the correct answer.
Detailed Explanation
First, find the vector sum: A + B = (3.0 - 2.5)i + (-4.5 + 5.0)j = 0.5i + 0.5j. Magnitude = √(0.5² + 0.5²) = √(0.25 + 0.25) = √0.5 = 0.707 N ≈ 0.71 N. The angle θ = tan⁻¹(0.5/0.5) = tan⁻¹(1) = 45°.
Hint
Add components separately, then find magnitude using Pythagorean theorem and direction using arctan(y/x).