Answer
a) See picture.
b) $-\boldsymbol{\hat{k}}$ (into the picture)
c) $ \vec{\boldsymbol{\tau}} = (-1.05 \, \mathrm{Nm}) \boldsymbol{\hat{k}} $
Work Step by Step
a) See picture.
b) Right hand rule for $\vec{\boldsymbol{\tau}} = \vec{\boldsymbol{r}} \times \vec{\boldsymbol{F}}$: Place fingers in direction of $\vec{\boldsymbol{r}}$, then curl them towards $\vec{\boldsymbol{F}}$. Thumb is then in the direction of $\vec{\boldsymbol{\tau}}$, into the picture (in this case).
c) $ \vec{\boldsymbol{\tau}} = \vec{\boldsymbol{r}} \times \vec{\boldsymbol{F}} =
\big( (-0.450 \, \mathrm{m}) \boldsymbol{\hat{\imath}} + (0.150 \, \mathrm{m}) \boldsymbol{\hat{\jmath}} \big) \times \big( (-5.00 \, \mathrm{N}) \boldsymbol{\hat{\imath}} + (4.00 \, \mathrm{N}) \boldsymbol{\hat{\jmath}} \big) =
\big( (-0.450 \, \mathrm{m})(4.00 \, \mathrm{N}) - (0.150 \, \mathrm{m})(-5.00 \, \mathrm{N}) \big) \boldsymbol{\hat{k}}=
(-1.05 \, \mathrm{Nm}) \boldsymbol{\hat{k}} $
Negative $z$-direction means that the vector points into the picture, as predicted in b).
