Write a MATLAB code that ask users enter two vectors vec$($a$)$ and vec

$($b$)$ in R$^3$ as inputs and it outputs five results:

Output $1$: dot product vec$($a$)*$vec$($b$)$

Output $2$: cross product vec$($a$)$ x vec$($b$)$

Output $3$: smallest angle among vectors

Output $4$: normal vector vec$($n$)$ as specified above

Output $5$: shortest distance D$0$ as specified above

Consider the vectors a $=(3,-1,7)$ and b $=(4,2,9)$ Answer the following questions:

$1.$ Evaluate the dot product a$.$ b$.$ Show all your steps. $[0\mathrm{.}5$ mark$]$

$2.$ Evaluate the cross producta $*$b Show all your steps. $[0\mathrm{.}5$ mark$]$

$3.$ Find the angle among the vectors using dot product. Show all your steps. $[0\mathrm{.}5$ mark$]$

$4.$ Find the angle among the vectors using cross product. Show all your steps. $[0\mathrm{.}5$ mark$]$

$5.$ Find the angle among the vectors using dot and cross products. Show all your steps. $[0\mathrm{.}5$ mark$]$

$6.$ Find a normal vector n to a plane that contains vec a and b has a direction ba and a magnitude of $3/5$ units. Show all your steps. $[0\mathrm{.}5$ mark$]$

$7.$ What is the shortest distance D$\_\{0\}$ between the heads of vectors vec a and b where these vectors are placed on the coordinate system in such a way that their tails coincide at the origin. Show all your steps. $[0\mathrm{.}5$ mark$]$

$8.$ Write a MATLAB code that ask users to enter two vectors overline a and b in $\backslash$mathbb$\{$R$\}^3$ as inputs and it outputs five results:

Output $1$: dot product overline ab

Output $2$: cross product ab

Output $3$: smallest an among vectors

Output $4$: normal vector overline n as specified above

Output $5$: shortest distance D$\_\{0\}$ as specified above.