Krivulje

Kako glase jednadžbe tangencijalnih ravnina plohe $\quad\vec{r}(u,v)=\left \{ u,u+v,u^2+v^2 \right \} \quad$ koje prolaze pravcem $\quad \frac{x-2}{2}=\frac{y-3}{3}=\frac{z-1}{10}.$

$\vec{r}(u,v)=$ $\displaystyle \left(u,\,u + v,\,u^{2} + v^{2}\right)$
$\vec{r}_{u}=$ $\displaystyle \left(1,\,1,\,2 \, u\right)$
$\vec{r}_{v}=$ $\displaystyle \left(0,\,1,\,2 \, v\right)$
$\vec{r}_{u}\times \vec{r}_{v}=$ $\displaystyle \left(-2 \, u + 2 \, v,\,-2 \, v,\,1\right)$
$\vec{p}=$ $\displaystyle \left(4,\,3,\,10\right)$
$\vec{N}\cdot\vec{p}=$ $\displaystyle -8 \, u + 2 \, v + 10$ $=0$
$v=4u-5$
$\vec{r}(u)=$ $\displaystyle \left(u,\,5 \, u - 5,\,{\left(4 \, u - 5\right)}^{2} + u^{2}\right)$
$\vec{N}(u)=$ $\displaystyle \left(6 \, u - 10,\,-8 \, u + 10,\,1\right)$
$A(x-x_{0})+B(y-y_{0})+C(z-z_{0})=0$
$T(2,3,10)$
$(6u-10)(2-u)+(-8u+10)(3-5u+5)+1-((4u-5)^2+u^2)=0$
[$\displaystyle u = \left(\frac{18}{17}\right)$, $\displaystyle u = 2$]
$\displaystyle 2 \, x - 6 \, y + z + 13$ $=0$
$\displaystyle -\frac{62}{17} \, x + \frac{26}{17} \, y + z + \frac{29}{17}$ $=0$
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
n(-0.053+4507228.4978+0.0039*0.000001*4507228.4978+0.0008*pi/(180*3600)*4369598.4978+0.00039*pi/(180*3600)*1067383.4978)
4.50722848134390e6
0.25+1
1.25000000000000
pi

Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1013, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> NameError: name 'PI' is not defined