PLEASE SOLVE C AND D FOR MY PYTHON CALCULUS $2$ PROJECT Problem $2$

Vectors and Geometry of Space

In a high$-$tech exploration team, Captain Li and her crew are preparing for an expedition to a newly discovered moon. Their navigation system requires precise calculations involving coordinates and vectors to identify safe landing zones. Two potential landing sites have been identified, represented by vectors. The first landing site $P$ is at the coordinates $P(1,-2,4)$ and the second landing site $Q$ is at $Q(3,1,6).$

c$)$ Understanding the angle between the vectors vec$(PQ)$ and vec$(D)$ is vital for Captain Li's navigation strategy. She needs to calculate this angle to assess the alignment of the two vectors.

$[5$ points$]$ Determine the unit vectors of vec$(PQ)$ and vec$(D).$

$[5$ points$]$ Determine the angle $$ between the vectors vec$(PQ)$ and vec$(D).$

d$)$ Captain Li wishes to visualize the following paraboloid equation in $3$D and draw the traces in the three coordinate planes $xy,yz,$ and $xz$ :

$\frac{x^2}{9}+\frac{y^2}{16}=z$

$-[15$ points$]$ Given the code to sketch a paraboloid, modify the code to match the provided equation. Draw the traces in the three coordinate planes $xy,yz,$ and $xz$ by hand, and explain the appearance of the resulting shapes$/$lines$.$