A $3-$dimensional right$-$handed orthogonal coordinate system, hat$(i)-$hat$(j)-$hat$(k),$ is defined. Given a vector

$\frac{?}{\text{b}\text{a}\text{r}}(W)$ with the following properties measured with respect to this reference frame.

$\frac{|}{b}ar(W{)}_P|=2,=30,=60$

Find: values of $w_1,w_2,w_3$ such that hat$(u{)}_W=\frac{w_1}{W}$hat$(i)+w_2$hat$(j)+w_3$hat$(k),$ where hat$(u{)}_W$ is the unit vector

pointing in the same direction as $\frac{?}{\text{b}\text{a}\text{r}}(W).($Hint: $\frac{?}{\text{b}\text{a}\text{r}}(W{)}_p$ is the projection of $\frac{?}{\text{b}\text{a}\text{r}}(W)$ down to the hat$(i)-$hat$(j)$ plane,

thus $$ does NOT measure directly between $\frac{?}{\text{b}\text{a}\text{r}}(W)$ and hat$(i).)$