Question

Displacement vector A points due east and has a magnitude of 2.26 km. Displacement vector B points due north and has a magnitude of 2.62 km. Displacement vector C points due west and has a magnitude of 2.6 km. Displacement vector D points due south and has a magnitude of 2.6 km. Find the magnitude and direction (relative to due east) of the resultant vector A + B + C + D.

Answer 1

Just add the vectors:
(2.26,0)
(0,2.62)
(-2.6,0)
(0,-2.6)
---------
(-0.34,-0.02) = 0.34 at W3.37°S

Answer 2

East (along x axis)
2.26 -2.60
so
-.34

North (along y axis)
2.62 -2.60
so
+.02

magnitude = sqrt (.34^2+.02^2)
= .341
direction (quadrant 2)
sin angle to x axis = .02/.341
so angle above negative x axis = 3.36 deg above -y axis

angle to + x axis = 180 -3.36 = 177 deg counterclockwise

angle to x axis clockwise (like a compass) = 180+3.36 = 183.3

Answer 3

By the way I bet you have at least one typo, but the method should work.

Answer 4

Thanks for checking
grumble grumble