194k views
3 votes
Let Iql = 5 at an angle of 45° and Irl = 16 at an angle of 300°.

What is |q - r|?
A. 13.0
B. 14.2
C. 15.5
D. 18.0
Keywords: trigonometry, absolute value, degrees, vector addition and subtraction, edge

1 Answer

4 votes

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.

User Moore
by
7.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.