physics
posted by thaokieu .
Before starting this problem, review Conceptual Example 7. The force vector A has a magnitude of 79.0 newtons (N) and points due east. The force vector B has a magnitude of 107 N and points 75.0 ° north of east. Find the (a) magnitude and (b) direction of A  B. (Give the direction as a positive angle with respect to due east). Find the (c) magnitude and (d) direction of B  A. (Give the direction as a positive angle with respect to due west).

Given: A = 79N, East; B = 107N @ 75deg.
a. X = hor. = 79  107cos75,
X = 79  27.7 = 51.3N.
Y = ver. = 0  107sin75,
Y = 0  103.4 = 103.4N.
M^2 = X^2 + Y^2,
M^2 = (51.3)^2 + (103.4)^2,
M^2 = 2631.7 + 10691.6 = 13323,
M = 115.4N Magnitude of AB.
b. tanA = Y/X = 103.4 / 51.3 = 2.015,
A = 63.6Deg. = 63.6deg South of East = Direction of AB.
Use the above procedure for BA.
Mag.= X/cosA = 106.7 / cos44.1 = 148.6N.
b. A = 79N,
B = 107N@75deg. = 107cos75 + i107sin75,
B = 27.7 + i103.4.
A  B = A to B = (27.7 + i103.4) 79,
A to B = 51.3 + i103.4
tan(theta) = 103.4 / 51.3 = 2.0156,
Theta = 63.6deg = 63.6deg South of East.
c. 
OOPS!!
Ignore data shown after part b.
It is incorrect.