#MrG 2017.1129 905 What Is The Dot Product?
#1) v.dot_product(w)=vx*wx+vy*wy
v=vector([2,-3])
w=vector([5,3])
show(v)
show(w)
show(v.dot_product(w))

#2) T/F: v.dot_product(w)==w.dot_product(v)?
show(w.dot_product(v))
show(bool(v.dot_product(w)==w.dot_product(v)))

#3) T/F: abs(v)==sqrt(v.dot_product(v))?
show(abs(v))
show(sqrt(v.dot_product(v)))

#4) T/F: abs(w)==sqrt(w.dot_product(w))?
show(abs(w))
show(sqrt(w.dot_product(w)))

#5) v.dot_product(w)==abs(v)*abs(w)*cos(t), find t?
var('t')
show(v.dot_product(w))
show(abs(v)*abs(w)*cos(t))
equ=v.dot_product(w)==abs(v)*abs(w)*cos(t)
show(equ)
show(((solve(equ,t)[0].rhs())*180/pi).n())
pv=plot(v,color='cyan')
pw=plot(w,color='magenta')
show(pv+pw,aspect_ratio=1)