$[25$ pts$]$ The curves vec$(r_1)(t)=($:$2cos(t),2sin(t),2t$:$)$ and vec$(r_2)(t)=($:$2+t,t,-t)$ intersect at the point $(2,0,0).$ Find the angle between the curves at this point of intersection.

$x=x_0+at$

$y=y_0+bt$

$z=z_0+ct$

$(x_0,y_0,z_0)=(30,0)$

vec$(n{)}_1=($:$2cos,2sin,z$:$)=($:$a,b,c$:$)$

L$1$:

$x=2+2cos(t)$

$y=0+2sin(t)$

$z=0+2t$

L $2$ :

$x=2+2+t$

$y=0+t$

$z=0-t$

vec$(n{)}_2=($:$2+t,t,-t$:$)=($:$a,b,c$:$)$

notrm $(n_1)$

$n_1{n}_2={?}^{ML}($:$-3\mathrm{.}68,13\mathrm{.}08,-5\mathrm{.}33$:$)$

norm $($n$2)$

$4.104$

b$.51$ rad

urves

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