Write comments in your programs, otherwise $2$ points will be deducted. For each program, the following info should at least be included at the top of the C file:

Author and Date created

Brief description of the program:

input$($s$)$ and output$($s$)$an algorithm $($or description$/$relationship between inputs and outputs$)$

Problem $2(35$ points$)$: Three$-$dimensional vector calculation

Given a vector V $=,$ its magnitude is calculated as

Given two vectors V$1=$ and V$2=,$

the dot product is

the angle $($in degrees$)$ between the two vectors is

Use $3\mathrm{.}14159$ for $.$

Write an interactive C program that

display options for vector calculation that a user can choose

ask a user for an option $($M$/$m for finding the magnitude, D$/$d for finding the dot product and angle between the two vectors, Q$/$q to Quit$)$

ask a user for one vector or two vectors $($depending on the option$)$

find and display the calculation

Your C program must use the following user defined function:

$//$ find$\_$magnitude accepts $3$ input arguments and returns the vector magnitude double find$\_$magnitude$($double Vx$,$ double Vy$,$ double Vz$)$;

For the function below, see zyBooks section $6\mathrm{.}2-$ pass by pointers

$//$ find$\_$dotprod$\_$angledeg accepts $2$ vectors and $//$ outputs the dot product and angle in degrees between two vectors void find$\_$dotprod$\_$angledeg$($double Vx$1,$ double Vy$1,$ double Vz$1,$ double Vx$2,$ double Vy$2,$ double Vz$2,$ double $*$dotprod$,$ double $*$angle$\_$deg$)$;

In the main code, let's assume it has double$-$type variables Vx$1,$ Vy$1,$ Vz$1,$ Vx$2,$ Vy$2,$ Vz$2,$ outputdotprod, outputangledeg, the function above is called with

find$\_$dotprod$\_$angledeg$($Vx$1,$ Vy$1,$ Vz$1,$ Vx$2,$ Vy$2,$ Vz$2,$ &outputdotprod, &outputangledeg$)$;

Sample code execution $1$:

$3-$D Vector calculation Enter M or m to find the magnitude Enter D or d to find the dot product and angle in degrees Enter Q or q to Quit Enter your choice: A wrong option entered $3-$D Vector calculation Enter M or m to find the magnitude Enter D or d to find the dot product and angle in degrees Enter Q or q to Quit Enter your choice: M Enter Vx Vy Vz $($separated by spaces$)$: $123\mathrm{.}3$ magnitude of $<1\mathrm{.}00,2\mathrm{.}00,3\mathrm{.}30>$ is $3\mathrm{.}98623-$D Vector calculation Enter M or m to find the magnitude Enter D or d to find the dot product and angle in degrees Enter Q or q to Quit Enter your choice: D Enter Vx$1$ Vy$1$ Vz$1($separated by spaces$)$: $123\mathrm{.}3$ Enter Vx$2$ Vy$2$ Vz$2($separated by spaces$)$: $7\mathrm{.}114\mathrm{.}223\mathrm{.}43<1\mathrm{.}00,2\mathrm{.}00,3\mathrm{.}30>$ dot $<7\mathrm{.}10,14\mathrm{.}20,23\mathrm{.}43>$ is $112\mathrm{.}8190$ angle between these $2$ vectors is $0\mathrm{.}0000$ degrees $3-$D Vector calculation Enter M or m to find the magnitude Enter D or d to find the dot product and angle in degrees Enter Q or q to Quit Enter your choice: m Enter Vx Vy Vz $($separated by spaces$)$: $7\mathrm{.}114\mathrm{.}223\mathrm{.}43$ magnitude of $<7\mathrm{.}10,14\mathrm{.}20,23\mathrm{.}43>$ is $28\mathrm{.}30223-$D Vector calculation Enter M or m to find the magnitude Enter D or d to find the dot product and angle in degrees Enter Q or q to Quit Enter your choice: q Good Bye

Sample code execution $2$:

$3-$D Vector calculation Enter M or m to find the magnitude Enter D or d to find the dot product and angle in degrees Enter Q or q to Quit Enter your choice: d Enter Vx$1$ Vy$1$ Vz$1($separated by spaces$)$: $123\mathrm{.}3$ Enter Vx$2$ Vy$2$ Vz$2($separated by spaces$)$: $117\mathrm{.}7-8<1\mathrm{.}00,2\mathrm{.}00,3\mathrm{.}30>$ dot $<11\mathrm{.}00,7\mathrm{.}70,-8\mathrm{.}00>$ is $0\mathrm{.}0000$ angle between these $2$ vectors is $90\mathrm{.}0001$ degrees $3-$D Vector calculation Enter M or m to find the magnitude Enter D or d to find the dot product and angle in degrees Enter Q or q to Quit Enter your choice: m Enter Vx Vy Vz $($separated by spaces$)$: $345$ magnitude of $<3\mathrm{.}00,4\mathrm{.}00,5\mathrm{.}00>$ is $7\mathrm{.}07113-$D Vector calculation Enter M or m to find the magnitude Enter D or d to find the dot product and angle in degrees Enter Q or q to Quit Enter your choice: D Enter Vx$1$ Vy$1$ Vz$1($separated by spaces$)$: $345$ Enter Vx$2$ Vy$2$ Vz$2($separated by spaces$)$: $-5\mathrm{.}41\mathrm{.}56<3\mathrm{.}00,4\mathrm{.}00,5\mathrm{.}00>$ dot $<-5\mathrm{.}40,1\mathrm{.}50,6\mathrm{.}00>$ is $19\mathrm{.}8000$ angle between these $2$ vectors is $70\mathrm{.}0592$ degrees $3-$D Vector calculation Enter M or m to find the magnitude Enter D or d to find the dot product and angle in degrees Enter Q or q to Quit Enter your choice: Q Good Bye