At what point do the curves r_1(t)=t,4-t,35+t^2 and r_2(s)=7-s,s-3,s^2Z

Consider the following curves:
${\displaystyle r_1\left(t\right)=<t,4-t,35+t^2>}$
${\displaystyle r_2\left(s\right)=<7-s,s-3,s^2>}$
Find the point of intersection of the curves and angle of intersection ${\displaystyle \theta }$.
The parametric equations corresponding to the curve ${\displaystyle r_1\left(t\right)}$ are as follows:
x=t
${\displaystyle y=4-t}$
${\displaystyle z=35+t^2}$
The parametric equations corresponding to the curve ${\displaystyle r_2\left(s\right)}$ are as follows:
${\displaystyle x=7-s}$
${\displaystyle y=s-3}$
${\displaystyle z=s^2}$
At the point of intersection of two curves, the corresponding coordinates of parametric lines are same.
${\displaystyle t=7-s\Rightarrow s+t=7}$
${\displaystyle 4-t=s-3\Rightarrow s+t=7}$
${\displaystyle 35+t^2=s^2\Rightarrow s^2-t^2=35}$
That is,
${\displaystyle s^2-t^2=35}$
${\displaystyle (s-t)(s+t)=35}$
${\displaystyle (s-t)7=35}$
${\displaystyle s-t=5}$
Solve the equations ${\displaystyle s-t=5}$ and ${\displaystyle s+t=7}$, to find the values of s and t.
${\displaystyle s-t+s+t=5+7\Rightarrow 2s=12\Rightarrow s=6}$
The corresponding value of t is as follows:
${\displaystyle t=7-s\Rightarrow t=7-6\Rightarrow t=1}$
Thus, the values are t=1 and s=6
Substitute t=1 in ${\displaystyle r_1\left(t\right)}$, to find the point of intersection.
${\displaystyle r_1\left(t\right)=<1,4-1,35+1^2\ge <1,3,36>}$
${\displaystyle r_1\left(t\right)=<1,3,36>}$
The angle between the normal vectors is given as ${\displaystyle \cos \theta =\frac{r_1^{\prime }\left(t\right)\cdot r_2^{\prime }\left(s\right)}{\left|r_1^{\prime }\left(t\right)\right|\left|r_2^{\prime }\left(s\right)\right|}}$
The direction vector of the line ${\displaystyle r_1\left(t\right)}$ is ${\displaystyle <t,-t,t^2>}$
The direction vector of the line ${\displaystyle r_2\left(s\right)}$ is ${\displaystyle <-s,s,s^2>}$
At t=1,
${\displaystyle r_1^{\prime }\left(t\right)=<1,-1,2t>}$
${\displaystyle r_1^{\prime }\left(1\right)=<1,-1,2>}$
At s=6,

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