Part A of this question asks for the sum of vector A = 3x+5y and vector B = 1x-3y. I did this and got the vector A + vector B = 4x+2y.

Question

Part B then asks what the magnitude and direction of vector A + vector B? The answer in the back of the textbook says that it is 4.5 at a 27 degree angle, but how do you get to this??

Answer 1

from the origin, 4 to the right and 2 up
so
tan (angle) = 2/4 = .5
so
angle = 26.57 degrees

Answer 2

sqrt (4^2 + 2^2) = sqrt (20) = 4.47