What is the approximate sum of the following two vectors: magnitude 10 at 120° and magnitude 15 at 90°?
A) magnitude 20 at 210°
B) magnitude 23 at 30°
C) magnitude 24 at 102°
D) magnitude 27 at 210°

Question

Quizplus · Accepted Answer

To find the sum of two vectors, we convert their polar forms into rectangular coordinates (x = r*cos(θ), y = r*sin(θ)), sum the coordinates, then convert back to polar form. For the first vector: x1 = 10*cos(120°) = -5, y1 = 10*sin(120°) = 8.66. For the second vector: x2 = 15*cos(90°) = 0, y2 = 15*sin(90°) = 15. Summing these gives x = -5 + 0 = -5, y = 8.66 + 15 = 23.66. Converting back to polar form gives a magnitude of approximately 24 and an angle of arctan(23.66/-5) ≈ 102° (adjusted for the correct quadrant).

What Is the Approximate Sum of the Following Two Vectors