### $1.$ Magnitude & Direction of Vector

Write a function m$-$file to find the magnitude and the direction of cosine of vector $**$F$**$ which expresses $3$ dimension $-$ $x$$,$ $y$$,$ and $z$$.$ Here are requirements for the function m$-$file.

$-$ Parameter$-$list $($input$($s$))$:

$-3$ dimensional vector

$-$ row vector or column vector $-$ undetermined

$-$ Return Value $($outputs$)$:

$-$ Magnitude of a given vector $-$ $$|\backslash$mathbf$\{\backslash$vec$\{$F$\}\}|=\backslash$sqrt$\{$F$\_$x$^2+$F$\_$y$^2+$F$\_$z$^2\}$$

$-$ Angles$($radian$)$ from direction of cosine $-$ $$\backslash$cos$(\backslash$alpha$)=\backslash$frac$\{$F$\_$x$\}\{|\backslash$mathbf$\{\backslash$vec$\{$F$\}\}|\},\backslash$cos$(\backslash$beta$)=\backslash$frac$\{$F$\_$y$\}\{|\backslash$mathbf$\{\backslash$vec$\{$F$\}\}|\},\backslash$cos$(\backslash$gamma$)=\backslash$frac$\{$F$\_$z$\}\{|\backslash$mathbf$\{\backslash$vec$\{$F$\}\}|\}$$

$-$ Order of outputs : $$[$Magnitude$,\backslash$alpha $,\backslash$beta $,\backslash$gamma $]$$

$-$ Function name : $***$Mag$\_$Vec$\_$yourEmailAccount$***$

Using a script m$-$file which will call the $***$Mag$\_$Vec$\_$yourEmailAccount$***$ function, save outputs with following given inputs.

$-$ If the given vector is $$**\backslash$mathbf$\{$F$\}\_1=2\backslash$hat$\{$i$\}3\backslash$hat$\{$j$\}6\backslash$hat$\{$k$\}$$$,**$ find the outputs of your $***$Mag$\_$Vec$\_$yourEmailAccount$***$ function. Then save the return values on $***$EX$1\_1.$dat$***.$

$-$ If the given vector is $$**\backslash$mathbf$\{$F$\}\_2=-4\backslash$hat$\{$i$\}2\backslash$hat$\{$k$\}$$$,**$ find the outputs of your $***$Mag$\_$Vec$\_$yourEmailAccount$***$ function. Then save the return values on $***$EX$1\_2.$dat$***.$

$-$ If the given vector is $$**\backslash$mathbf$\{$F$\}\_3=3\backslash$hat$\{$i$\}+4\backslash$hat$\{$j$\}$$$,**$ find the outputs of your $***$Mag$\_$Vec$\_$yourEmailAccount$***$ function. Then save the return values on $***$EX$1\_3.$dat$***.$

$-$ If the given vector is $$**\backslash$mathbf$\{$F$\}\_4=5\backslash$hat$\{$j$\}+12\backslash$hat$\{$k$\}$$$,**$ find the outputs of your $***$Mag$\_$Vec$\_$yourEmailAccount$***$ function. Then save the return values on $***$EX$1\_4.$dat$***.$

$-$ If the given vector is $$**\backslash$mathbf$\{$F$\}\_5=\backslash$hat$\{$i$\}+\backslash$hat$\{$j$\}+\backslash$hat$\{$k$\}$$$,**$ find the outputs of your $***$Mag$\_$Vec$\_$yourEmailAccount$***$ function. Then save the return values on $***$EX$1\_5.$dat$***.$