Vector a has a magnitude of 5.2 and is directed east. Vector b has a magnitude of 4.3 units and is directed 35

Question

Vector a has a magnitude of 5.2 and is directed east. Vector b has a magnitude of 4.3 units and is directed 35o west of north. By constructing vector diagrams, find the magnitudes and direction of (a) a + b, and (b) a – b

Answer 1

Using Cartesian coordinates:

a = (5.2, 0)
b = (-4.3*sin35, 4.3*cos35) = (-2.47, 3.52)

a + b = (2.74, 3.52) => magnitude = sqrt(2.74^2+3.52^2) = 4.46, angle = atan(2.74/3.52) = 37.84 o from the North to the East.
a - b = (7.67, -3.52) => magnitude = sqrt(7.67^2+3.52^2) = 844, angle = atan(7.67/3.52) = 65.35 o from the South toward the East.

Answer 2

I agree with Fernando_007