Physics Vectors?

Three vectors a, b, and c, each have a magnitude of 42 m and lie in an xy plane. Their directions relative to the positive direction of the x axis are 27 ˚, 194 ˚, and 312 ˚, respectively. B) i need the angle of the vector a+b+c (relative to the +x direction in the range of (-180°, 180°) i got 42 but its not correct do i have to add it to 180? D)angle of a-b+c in the range of (-180°, 180°) i got 5 degrees for this. and it is incorrect

1 Answer
Jun 4, 2018

#-130#
Visualizing the compass for the angles helps.

Explanation:

With equal magnitude vectors it may be even easier to visualize, but the angles work in all cases. A vector result is a combination of the component vector directions as well as the magnitudes.
Looking at a compass you can see the necessary movements of the pairs of angles.

Because they are additive, we can do them in pairs. The combination of the two large angles would result in an average of #(312 - 194)/2 + 194 = 253#. The second combination is the average of the range from this average to 360, plus the given angle:
#((360 - 253) + 27)/2 + 253 = 320#

In terms of a +/- 'x' axis direction that is (360 - 320) = 40 degrees NEGATIVE of 90 (vertical), or 50 degrees Positive from -180 (again, look at a coordinate plane with your compass).
So, in the terms desired, that would be an angle of #-130#