#$1.$ Given the line L:a$=$d$-3$t$,$ y $=62+$t$,$ z$=5$t and the point P$(0,0,3)($not onthe line$)$ do:$($a$)$ Find the equation of the plane H that is perpendicular to L and contains P$.($b$)$ Find the point $($Q where the line L intersects the plane H$.($First find the value of t$.)($c$)$ True or False, Justify. Let d be the distance from the point P to the plane H$,$ is thisthe same as the distance from P to Q$?($Note that Plies on H$,$ and PQ$)$#$2.$ Given the elliptic paraboloid$($b$)$ Let C be the curve which is the intersection of the above elliptic paraboloid withthe plane $2*+$ y $=3$ Find a parametrization of C as a vector function r$($t$)=($z$($t$),$ y$($t$),($t$)).$ Simplify your answer$\mathrm{.}4$#$3.$ Given points P$(0,-2,1),$ Q$5,0,3),$ R$(0,1,0)$ do:$($a$)$ Find an equation of the plane that contains P$,$ Q$,$ R$.($b$)$ Find the area of the triangle with vertices P$,$ Q$,$ R$.$#$4.$ In the ry$-$plane given the vector u $(8,-6)$ and the vector v $=(1,$ I$)$ do$($a$)$ Find the unit vector s $=($b$)$ find comp,u $($scalar component$),45.$ Given the curve C with vector equation r$()=($cos$(-$t$),$t$)$ do:$($a$)$ find the point P on the curve corresponding to t$-$T$($b$)$ find the velocity vector v$($t$)($as a vector function depending on $),($c$)$ Evaluate the velocity vector when t$=-($d$)$ Find the equation of the tangent line to the curve when t#$6($cont$.$ from #$5,$ use what was given in #$5,$ and what you already found$).($a$)$ find the acceleration a$($t$)$ when$($b$)$ True or False, Justify. Is it true that v$()$ is orthogonal to a$()?$#$7($pacing back and forth$)($a$)$ Eliminate the parameter to find a Cartesian equation ofthe planar curve C given by the parametric equationsa$=($sin t$)=$ sin$($t$),$y$=(2$ cos $($t$))4$ cos $(4)($b$)$ Is this curve an ellipse or not? Is it a ine, is it a ine segment? What is the rangeof values that z takes on; what values does y take on$?)($c$)$ Sketch the curve C in the plane.y$+$ do: $($a$)$ sketch it$,($c$)$ find proj,u $($vector projection$).$t$,($ie$.,$ find a$-)),$