ssign your student number to the variable Ex$1$Anum. $($Note: we are asking for a number

like $87654321$ and not text with quotation marks as in $"87654321".)$

$($b$)$ Enter the first $3$ digits of your student number as a $($row$)$ vector and save the result as

Ex$1$Bvec. For example, if your student number is $87654321$ then we are asking for the

vector $(8,7,6).$

$($c$)$ Compute the length of the vector in $($b$)$ and save the result as Ex$1$Cnum.

$($d$)$ Enter the first $3$ digits of your student number as a vector v and enter the last $3$ digits

of your student number as a vector w$.$ Compute the projection of v onto w and save

the result as Ex$1$Dvec. For example, if your student number is $87654321$ then we are

asking for the projection of $(8,7,6)$ onto $(3,2,1).$

Exercise $2$

The centroid of a triangle is the arithmetic mean of the vertices. In other words, if A$,$ B and

C are the vertices of a triangle then the centroid is given by

$1$

$3($A $+$ B $+$ C$)$

$($a$)$ Compute the centroid O of the triangle with vertices A $=(4,1),$ B $=(2,5)$ and

C $=(3,4)($see figure below$)$ and save the result as Ex$2$Avec.

$($b$)$ Find the vector from O to A and save the result as Ex$2$Bvec.

$($c$)$ Find the vector from O to C and save the result as Ex$2$Cvec.

$($d$)$ Find the angle $\backslash$angle AOC and save the result as Ex$2$Dnum. Use the dot product formula

v $$ w $=$v$$w$$ cos $\backslash$theta

$1$

Exercise $3$

We can visualize the geometry of vectors in $2$D and $3$D space as arrows but this is not

possible in higher dimensions. Instead we can visualize vectors in higher dimensions using

bar plots where the x$-$axis represents the index and the y$-$axis is the value of each entry. For

example:

$>>$ v$1=[+1-1+1-1+1-1+1-1+1-1]$;

$>>$ bar$($v$1),$ grid on$,$ ylim$([-2+2])$

$2$

$>>$ v$2=[+1+1-1-1+1+1-1-1+1+1]$;

$>>$ bar$($v$2),$ grid on$,$ ylim$([-2+2])$

$>>$ w $=[1234554321]$;

$>>$ bar$($w$),$ grid on$,$ ylim$([-1+6])$

$($a$)$ Compute the projection of w onto v$1$ and save the result as Ex$3$Avec.

$($b$)$ Compute the projection of w onto v$2$ and save the result as Ex$3$Bvec.

$($c$)$ Is the vector w perpendicular to v$1?$ Save your response as Ex$3$Ctext $=$ "yes" or

Ex$3$Ctext $="$no$".$

$($d$)$ Is the vector w perpendicular to v$2?$ Save your response as Ex$3$Dtext $=$ "yes" or

Ex$3$Dtext $="$no$".$