Get the resultant of the following displacement 6 ft. southwest; 10 ft. north-east; 4 ft. south-east; 12 ft. northwest and 3 ft. southwest. What is the direction of the resultant displacement?

Answer 1

For all of these directions, the x-y displacements are 1/√2 times the distance traveled, so starting at (0,0), you end up at
1/√2 (-6+10+4-12-3 , -6+10+4+12-3) = 1/√2 (-7,17)
The direction, measured from due east, is thus θ, where
tanθ = 17/-7 = 112.3° or N 22.3° W or a heading of 337.7°