HOMEWORK $8\mathrm{.}1$: Vector Magnitude

Write a function that can take the rectangular components of a $3$D vector and returns the vector magnitude.

$A_{3D}=A_x$hat$()+A_y$hat$()+A_z$widehat$(k),|A_{3D}|=\sqrt[\phantom{2}]{A_x^2+A_y^2+A_z^2}$

However, if the user only passes $2$ values to the function, assume the vector is a $2$D vector and return the magnitude of that.

$A_{2D}=A_x+A_y$hat$(),|A_{2D}|=\sqrt[\phantom{2}]{A_x^2+A_y^2}$

Eunction vectorMagnitude $(x,y,$ Optional $z)$

vectorMagnitude $=[$ magnitude$]$

End Function

$\backslash$table$[[Ax,4,Ax,3],[Ay,4,Ay,4],[Az,7,|A|,],[|A|,,,]]$

functions available from the

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Check your answers. Here is an example of what you should get for the given inputs.

HOMEWORK $8\mathrm{.}2$: Volume and Surface Area of a Torus

In geometry, a torus is a surface of revolution generated by revolving a circle in threedimensional space one full revolution about an axis that is coplanar with the circle.

$V=(2R)(r^2)=2{}^{2}R{r}^2$

The surface area is given as:

$SA=(2R)(2r)=4{}^{2}Rr$

Write $2$ functions, one that calculates the volume of a torus, and one that calculate the surface area of a torus given the $2$ radii defined above.

The instructor is going to pull up your module and read your code. For full credit, your code needs to have the proper header and be neatly commented. You will only get partial credit if your code works but is not clear.