# Example 2.1
MKS(N, deg)
f1 = PolarVec(100 N, 15 deg)
f2 = PolarVec(150 N, 80 deg)
f3 = f1 + f2
mag(f3)
PolarAngle(f3)

# Example 2.2
IPS()
f1 = PolarVec(200 lbf, 40 deg)
fxp = 200 lbf * sin(50 deg) / sin(60deg)
fyp = 200 lbf * sin(70 deg) / sin(60 deg)

# Example 2.3
MKS()
f1 = 500 N
f2 = 400 N
q1 = 60 deg
q2 = asin(sin(q1) * f2 / f1); deg
q2p = 180 deg - q1 - q2; deg

# Example 2.4
MKS(N)
f0 = 1000 N
q0 = 130 deg
q1 = 30 deg
f1 = f0 * sin(q1) / sin(q0)
q2 = 20 deg
f2 = f0 * sin(q2) / sin(q0)
# b
q3 = 70 deg;
PolarVec(f0, q3)

# Example 2.5
MKS(N)
f1 = PolarVec(200 N, 120 deg)
f2 = PolarVec(260 N, -atan(5/12))

# Example 2.6
MKS(N)
f1 = PolarVec(600 N, 30 deg)
f2 = PolarVec(400 N, 135 deg)
f3 = f1 + f2
mag(f3)
PolarAngle(f3); deg

# Example 2.7
MKS(N)
f1 = PolarVec(400 N, 180 deg)
f2 = PolarVec(250 N, 45 deg)
f3 = PolarVec(200 N, 180 deg - atan(3/4))
f4 = f1 + f2 + f3
mag(f4)
PolarAngle(f4); deg

# Example 2.8
MKS(N, deg)
q1 = 60 deg
q2 = 45 deg
q3 = acos(sqrt(1 - cos(q1)^2 - cos(q2)^2))
f = 200 N
f_vec = f * [cos(q3), cos(q1), cos(q2)]

# Example 2.9
IPS(deg)
f1 = [0, 60, 80] lbf
f2 = [50, -100, 100] lbf
fr = f1 + f2
mag(fr)
u = fr / mag(fr)
acos(u[1])
acos(u[2])
acos(u[3])

# Example 2.10
IPS(deg)
q1 = 60 deg
q2 = 45 deg
f1 = 100 lbf
f2 = 300 lbf
f1z = f1 * sin(q1)
ff = f1 * cos(q1)
f1x = ff * cos(q2)
f1y = -ff * sin(q2)
f_vec = [f1x, f1y, f1z]
mag(f_vec)
u = f_vec / mag(f_vec)
acos(u[1])
acos(u[2])
acos(u[3])

# Example 2.11
MKS(deg)
a1 = 45 deg
b1 = 60 deg
g1 = 120 deg
f1 = 300 N * [cos(a1), cos(b1), cos(g1)]
fr = 800 N * [0, 1, 0]
f2 = fr - f1
mag(f2)
u = f2 / mag(f2)
acos(u[1])
acos(u[2])
acos(u[3])

# Example 2.12
MKS(deg)
x1 = [-2, 2, 3] m
x2 = [1, 0, -3] m
rr = x1 - x2
mag(rr)
u = rr / mag(rr)
acos(u[1])
acos(u[2])
acos(u[3])

# Example 2.13
FPS(deg)
x1 = [12, -8, 6] ft
x2 = [0, 0, 30] ft
rr = x1 - x2
mag(rr)
u = rr / mag(rr)
acos(u[1])
acos(u[2])
acos(u[3])

# Example 2.14
MKS(deg)
x1 = [1.707, 0.707, 0] m
x2 = [0, 0, 2] m
rr = x1 - x2
mag(rr)
u = rr / mag(rr)
acos(u[1])
acos(u[2])
acos(u[3])
f = 500 N * u

# Example 2.15
MKS(N, deg)
fab = 100 N
fac = 120 N
xb = [4, 0, 0] m
xa = [0, 0, 4] m
xc = [4, 2, 0] m
rab = xb - xa
rac = xc - xa
fr = fab * rab / mag(rab) + fac * rac / mag(rac)
mag(fr)
u = fr / mag(fr)
acos(u[1])
acos(u[2])
acos(u[3])

# Example 2.16
MKS(N, deg)
f = [0, 300, 0] N
rb = [2, 6, 3] m
ub = rb / mag(rb)
fab = dot(f, ub) * ub
f_perp = f - fab
mag(fab)
mag(f_perp)

# Example 2.17
FPS(deg)
rba = [-2, -2, 1] ft
rbc = [0, -3, 1] ft
q = acos(dot(rba, rbc) / (mag(rba) * mag(rbc))); deg
uba = rba / mag(rba)
f0 = 80 lbf
f = f0 * rbc / mag(rbc)
fba = dot(f, uba)
f_perp = f0 * sin(q)
sqrt(f0^2 - fba^2)

# Homework Problems:

TBD