Krivulje

Kako glase jednadžbe tangencijalnih ravnina plohe koje prolaze pravcem

u,v,y,z=var('u,v,y,z')

r=vector((u,u+v,u^2+v^2))
ru=diff(r,u)
rv=diff(r,v)
show('$\\vec{r}(u,v)=$',r)
show('$\\vec{r}_{u}=$',ru)
show('$\\vec{r}_{v}=$',rv)
rurv=ru.cross_product(rv)
show('$\\vec{r}_{u}\\times \\vec{r}_{v}=$',rurv)
p=vector((4,3,10))
show('$\\vec{p}=$',p)
np=rurv.dot_product(p)
show('$\\vec{N}\\cdot\\vec{p}=$',np,'$=0$')
show('$v=4u-5$')
ruu=r(v=4*u-5)
show('$\\vec{r}(u)=$',ruu)
Nu=rurv(v=4*u-5)
show('$\\vec{N}(u)=$',Nu)
show('$A(x-x_{0})+B(y-y_{0})+C(z-z_{0})=0$')
show('$T(2,3,10)$')
show('$(6u-10)(2-u)+(-8u+10)(3-5u+5)+1-((4u-5)^2+u^2)=0$')
show(solve((6*u-10)*(2-u)+(-8*u+10)*(3-5*u+5)+1-((4*u-5)^2+u^2),u))
show(((6*u-10)*(x-u)+(-8*u+10)*(y-5*u+5)+z-((4*u-5)^2+u^2))(u=2),'$=0$')
show(((6*u-10)*(x-u)+(-8*u+10)*(y-5*u+5)+z-((4*u-5)^2+u^2))(u=18/17),'$=0$')


[, ]
u,v=var('u,v')
parametric_plot3d((u,u+v,u^2+v^2),(u,-10,10),(v,-10,10),color='green',frame=false)+parametric_plot3d((4*u+2,3*u+3,10*u+1),(u,-10,10),color='red',frame=false)+implicit_plot3d(2*x-6*y+z+13==0,(x,-50,50),(y,-50,50),(z,-50,50),opacity=.40)+implicit_plot3d(-62*x+26*y+17*z+29==0,(x,-50,50),(y,-50,50),(z,-50,50),opacity=.40)

3D rendering not yet implemented
u,v,y,z=var('u,v,y,z')

r=vector((v,(3*u+2*v)/(u+v),2*u))
ru=simplify(diff(r,u))
show(ru(u=1,v=-2))
ruv=simplify(diff(ru,v))
show(ruv(u=1,v=-2))
rv=simplify(diff(r,v))
show(rv(u=1,v=-2))
rvu=simplify(diff(rv,u))
show(rvu)