907 MrG How do we find the Cross Product?

2758 days ago by MATH4R2013

#9 p629 find the area of the parallelogram formed by u and w #9 p629 given u=<2,-3,1> and w=<3,-2,-1> v=vector([2,-3,1]) w=vector([3,-2,-1]) c1=v.cross_product(w) c2=w.cross_product(v) show(v) show(w) show(c1) show(c2) show(abs(c1)) show(abs(c2)) p1=plot(v,color='red') p2=plot(w,color='green') p3=plot(c,color='cyan') show(p1+p2+p3,aspect_ratio=1) 

#31 p629 find the volume of the parallelepiped formed by v,u and w #31 p629 such that v=<-3,3,2>, u=<2,-3,1> and w=<1,1,3> #31 p629 ie: find v(u x w) v=vector([-3,3,2]) u=vector([2,-3,1]) w=vector([1,1,3]) c=u.cross_product(w) s=v.dot_product(c) show(v) show(u) show(w) show(c) show(s) p1=plot(v,color='red') p2=plot(u,color='green') p3=plot(w,color='cyan') show(p1+p2+p3,aspect_ratio=1) 

#39 p629 v.cross_product(w)=abs(v)*abs(w)*sin(t) #39 p629 find t if v=<1,2,3> and w=<-2,3,0> v=vector([1,2,3]) w=vector([-2,3,0]) c=v.cross_product(w) show(v) show(w) show(c) show(arcsin(abs(c)/abs(v)/abs(w)).n()) show((arcsin(abs(c)/abs(v)/abs(w))*180/pi).n()) p1=plot(v,color='red') p2=plot(w,color='green') p3=plot(c,color='cyan') show(p1+p2+p3,aspect_ratio=1)