Question Detail
Question
The resultant of two vectors A and B is vector C = 2.2i + 3.4j. If vector A = 1.5i - 2.0j, find the magnitude of B and the angle it makes with the positive x-axis.
Correct Answer
Option D is the correct answer.
Detailed Explanation
Since C = A + B, then B = C - A = (2.2i + 3.4j) - (1.5i - 2.0j) = (2.2 - 1.5)i + (3.4 + 2.0)j = 0.7i + 5.4j. Magnitude |B| = √(0.7² + 5.4²) = √(0.49 + 29.16) = √29.65 = 5.44 units. This doesn't match the options. If A = 1.5i - 2.0j and C = 2.2i + 3.4j, then B = (0.7i + 5.4j). |B| = √(0.49 + 29.16) = √29.65 = 5.44. Angle θ = tan⁻¹(5.4/0.7) = tan⁻¹(7.714) = 82.6°. None of the options have 5.44. Option D says 4.02 units, 7.4°. Possibly there's a misprint in the problem or options.
Hint
B = C - A. Then find magnitude using √(B_x² + B_y²) and angle using tan⁻¹(B_y/B_x).