# Example 2.1
Fab = PolarVEc(100 kN, 30 deg)
Fac = PolarVEc(60 kN, 0 deg)
F0 = Fab + Fac
mag(F0); kN
PolarAngle(F0); deg


# Example 2.2
FPS
Fw[2] = -600 lb
Fd = [-200, 100] lb
Fl = -Fw -Fd
Fdouble = Fw + 2 * Fd + Fl
mag(Fdouble)


# Example 2.3
FPS
Fab = PolarVec(4000 lb, (180 - 30) deg)

# Example 2.4
MKS(N, deg)
q = atan(0.5)
f = PolarVec(800 N,  90 deg -q)

# Example 2.5
FPS
Fa = PolarVec(100 lb, 50 deg)
BEGIN
   fb = 1 lb
   Fb = PolarVec(fb, -70 deg)
   fy = Fa[2] + Fb[2]
END
solve(fy,fb)


# Example 2.6
xd = [2, 3, 1] m
xc = [4, 0, 0] m
rdc = xd - xc
mag(rdc)

# Example 2.7
FPS(deg)
qx = 54 deg
qy = 40 deg
qz = acos(sqrt(1 - cos(qx)^2 - cos(qy)^2))
f = 600 lb
fx = f * cos(qx)
fy = f * cos(qy)
fz = f * cos(qz)


# Example 2.8
MKS(N, deg)
qx = 60 deg
qy = 45 deg

f = 800 N
fy = f * sin(qy)
fh = f * cos(qy)

fx = fh * sin(qx)
fz = fh * cos(qx)


# Example 2.9
MKS(N)
rb = [800, 500, -300] mm
ra = [200, 200, -100] mm
rba = rb - ra
mag(rba)
eba = rba / mag(rba)
f = 140 N * eba


# Example 2.10
FPS
ra = [6, 7, 0] ft
rb = [2, 0, 4] ft
rc =[12, 0, 6] ft

rba = rb - ra
rca = rc - ra

eba = rba / mag(rba)
eca = rca / mag(rca)

f = 200 lb 
fba = f * eba
fca = f * eca

ff = fba + fca
mag(ff)



# Example 2.11
MKS(N)
rc = [0.2, 0, 0.25] m
rd = [0.4, 0.3, 0] m
rcd = rc - rd
ecd = rcd / mag(rcd)
rca = 0.2 m * ecd
roc = [0.4, 0.3, 0] m
roa = roc + rca

ra = [0, 0.5, 0.15] m

rab = ra - roa
eab = rab / mag(rab)
tt = 50 N * eab


# Example 2.12

ra = [4, 3, 2] m
rb = [6, 1, -2] m
rc = [8, 8, 4] m
rba = rb - ra
rca = rc - ra
mag(rba)
mag(rca)
d = dot(rba, rca)
acos(dot(rba, rca) / (mag(rba) * mag(rca))); deg


# Example 2.13
MKS(N)
ra = [6, 6, -3] m
rb = [10 , -2, 3] m
ea = ra / mag(ra)
eb = rb / mag(rb)
f = 50 N
ff = f * ea
dot(eb, ff)
fp = dot(eb, ff) * eb
fn = ff - fp


# Example 2.14
FPS
f = PolarVec(100 lb, 0 deg)
r = PolarVec(8 ft, 60 deg)
cross(r, f)



# Example 2.15
ra = [10, -2, 3] m
rb = [6, 6, -3] m
x = cross(ra, rb)
e = x / mag(x)

sinq = mag(x) / (mag(ra) * mag(rb))
d = mag(ra) * sinq



# Example 2.16
ra = [0.5, 0, 0] m
rb = [0.35, 0, 0.2] m
rc = [0, 0.2, 0] m
re = [0.2, 0.4, -0.1] m


x = cross(rb - rc, ra- rc)
e = x / mag(x)
rec = re - rc
t = 500 N
tt = t * rec / mag(rec)
dot(e, tt) * e

# Homework Problems:

TBD