Final answer:
To find the absolute difference between q and r, convert the given vectors from polar form to rectangular form. Subtract the two vectors and find the magnitude of the resulting vector. The absolute difference between q and r is approximately 21.2.
Step-by-step explanation:
To find the absolute difference between q and r, we need to first convert the given vectors from polar form to rectangular form. Let's convert Iql = 5 at an angle of 45° to rectangular form: Iql = 5 cos(45°)î + 5 sin(45°)ĵ = 3.536î + 3.536ĵ. Next, let's convert Irl = 16 at an angle of 300° to rectangular form: Irl = 16 cos(300°)î + 16 sin(300°)ĵ = -8î - 13.856ĵ.
Now, we can subtract the two vectors: q - r = (3.536 - (-8))î + (3.536 - (-13.856))ĵ = 11.536î + 17.392ĵ. Finally, we can find the magnitude of the resulting vector: |q - r| = sqrt((11.536)^2 + (17.392)^2) = 21.155. Therefore, the absolute difference between q and r is approximately 21.2. The correct answer choice is B. 14.2.