preTEST9

3115 days ago by MATH4R2012

#page1) u=vector([1,0,1]);show(u) v=vector([0,-2,6]);show(v) w=vector([0,4,2]);show(w) 
       


#1) diff=u-v;show(diff) 
       
#2) dilate1=3*(u-v);show(dilate) 
       
#3) sum=u+w;show(sum) 
       
#4) dilate2=(-1/2)*(u+w);show(dilate2) 
       
#5) ans=dilate1+dilate2;show(ans) 
       
#extra u1=plot(u,color='red') v1=plot(v,color='green') s1=plot(sum,color='blue') d1=plot(diff,color='brown') u1+v1+s1+d1 
       
#page2) u=vector([1,-2,5]);show(u) v=vector([-3,1,-1]);show(v) 
       

#6) dilate1=2*u;show(dilate1) 
       
#7) dilate2=2*v;show(dilate2) 
       
#8) sum=dilate1+dilate2;show(sum) 
       
#9) ans=2*(u+v);show(ans) 
       

#10)

Distribution!

2(u+v)=2u+2v

#11) l1=line([(2,5),(1,6)]) l2=line([(1,6),(1,1)]) l3=line([(1,1),(2,5)]) plot(l1+l2+l3,aspect_ratio=1) 
       
#12) ab=vector([1-2,6-5]);show(ab) ac=vector([1-2,1-5]);show(ac) ab1=plot(ab,color='red') ac1=plot(ac,color='green') (ab1+ac1).show(aspect_ratio=1) 
       


#13) dot=ab*ac;show(dot) 
       
#14)ab*ac=abs(ab)*abs(ac)cos(A) angA=arccos(dot/abs(ab)/abs(ac)) show(abs(ab)) show(abs(ac)) show(angA) show(angA.n()) show((180/pi*angA).n()) 
       




#15)K=(1/2)*abs(ab)*abs(ac)*sin(angA) area=(1/2)*abs(ab)*abs(ac)*sin(angA) show(area) show(area.n()) 
       

#16) #11) l1=line([(0,1),(3,0)]) l2=line([(3,0),(4,4)]) l3=line([(4,4),(1,5)]) l4=line([(1,5),(0,1)]) plot(l1+l2+l3+l4,aspect_ratio=1) 
       
#17) cd=vector([1-4,5-4,0]);show(cd) cb=vector([3-4,0-4,0]);show(cb) 
       

#18) cross=cd.cross_product(cb);show(cross) cd1=plot(cd,color='red') cb1=plot(cb,color='green') cross1=plot(cross,color='blue') cd1+cb1+cross1 
       
#19)abs(cross)=abs(cd)*abs(cb)*sin(angC) angC=arcsin(abs(cross)/abs(cd)/abs(cb)) show(angC) show(angC.n()) show((180/pi*angC).n()) 
       


#20) (.5)*abs(cross)