Forces $\mathbf{F}$, $\mathbf{P}$, and $\mathbf{T}$ are concurrent and acting in the direction as shown.
- Find the value of $F$ and $\alpha$ if $T$ = 450 N, $P$ = 250 N, $\beta$ = 30°, and the resultant is 300 N acting up along the $y$-axis.
- Find the value of $F$ and $\alpha$ if $T$ = 450 N, $P$ = 250 N, $\beta$ = 30° and the resultant is zero.
- Find the value of <$\alpha$ and $\beta$ if $T$ = 450 N, $P$ = 250 N, $F$ = 350 N, and the resultant is zero.