Is This The Correct Answer?

Question

Add: -3∠-125° + 7∠115°

(A) -1.24 R + 8.80 U

(B) 3.89 R - 4.68 U

(C) -4.68 R + 8.80 U

(D) 0.15 R + 1.73 U

(E) None of the above

For this I got; (A) -1.24 R + 8.80 U. Is this correct?

Answer 1

I am unfamiliar with a vector notation of R and U. However, assuming that the give vectors are in polar notation of (r, θ) and we are converting them to rectangular coordinates x, y then you are correct.

The vector (r, θ) (-3, -125°) can be converted to a more normal notation by first converting the angle to a positive by adding 360° so it becomes (-3, 235) then flipping the radius to a positive by subtracting 180° to the angle gives (3, 55°)

The rectangular components of this are x: rcos(θ) = 3cos(55) = 1.721 and y: rsin(θ) = 3sin(55) = 2.457

The other vector (r, θ) (7, 115°) has rectangular components of x: rcos(θ) = 7cos(115) = -2.958 and y: rsin(θ) = 7sin(115) = 6.344

Adding the two x values gives: 1.721 - 2.958 = -1.24

Adding the two y values gives: 2.457 + 6.344 = 8.80

So if the unit vector in the x direction were R and the unit vector in the y direction were U, then your answer is correct.