## University Physics with Modern Physics (14th Edition)

a) See picture. b) $-\boldsymbol{\hat{k}}$ (into the picture) c) $\vec{\boldsymbol{\tau}} = (-1.05 \, \mathrm{Nm}) \boldsymbol{\hat{k}}$ 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).