n $6$

Let vec$(i),$vec$(j)$ and vec$(k)$ denote the standard basis vectors of $R^3.$

Let

vec$(u)=-$vec$(j)+2$vec$(k)$ and vec$(v)=-$vec$(i)-3$vec$(j)+$vec$(k)$

a$)$ Calculate the following orthogonal projection:

$pro{j}_{\text{v}\text{e}\text{c}(u)}(vec(v))=$

$a^b$

$\frac{a}{b}$

$\sqrt[\phantom{2}]{a}$

$|a|$

$$

$sin(a)$

$-j+2k$

FORMATTING: Write your answer in the form $Ai+Bj+Ck.$ eg$,3i+2k$ or $\frac{2i+3j-5k}{4}.$ Do not put arrows on the vectors $i,j$ and $k.$

b$)$ What is the angle $($in radians$)$ between vec$(u)$ and vec$(v)?$

$=$ rad