Two cables with forces $\frac{?}{\text{b}\text{a}\text{r}}(F)$ and $\frac{?}{\text{b}\text{a}\text{r}}(T)$ pulling on point $C$ keep the flag pole in the vertical position. The direction angle of $\frac{?}{\text{b}\text{a}\text{r}}(T)$ with respect to the $z-$axis is

$$

The direction cosine of $\frac{?}{\text{b}\text{a}\text{r}}(T)$ with respect to the $y-$axis is

If the magnitudes of the first two components of $\frac{?}{\text{b}\text{a}\text{r}}(F)$ are $0\mathrm{.}63kN$ and $0\mathrm{.}23kN,$ and if $\frac{|}{b}ar(F)|=1kN,$ complete the representation by adding the appropriate signs for all three components, the magnitude of the last component, and the relevant unit. A unit vector in the opposite direction of $F$ is

$(\frac{,}{b}ar(i)+\frac{,}{b}ar(j)+\frac{,}{b}ar(k))$

Calculate the coordinates of point $A.$

$A=(,0)m$ If $\frac{|}{b}ar(T)|=1\mathrm{.}9kN,$ the cartesian vector representation of $\frac{?}{\text{b}\text{a}\text{r}}(T)$ is given by

$\frac{?}{\text{b}\text{a}\text{r}}(T)=(\frac{1\mathrm{.}017}{b}ar(i)+\frac{0\mathrm{.}8413}{b}ar(j)-\frac{1\mathrm{.}367}{b}ar(k))kN$

Calculate the cartesian vector form of the projection $\frac{?}{\text{b}\text{a}\text{r}}(P)$ of $\frac{?}{\text{b}\text{a}\text{r}}(T)$ on the line of action of $\frac{?}{\text{b}\text{a}\text{r}}(F).$

$\frac{?}{\text{b}\text{a}\text{r}}(P)=(\frac{,}{b}ar(i)+\frac{,}{b}ar(j)+\frac{,}{b}ar(k))$

The corresponding component of the projection $\frac{?}{\text{b}\text{a}\text{r}}(P)$ calculated in part $($f$)$ is

$([\frac{?}{\text{b}\text{a}\text{r}}(i)+\frac{,}{b}ar(j)+\frac{,}{b}ar(k))]$