Question: A physics Brady Bunch, whose weights in newtons are indicated in Fig.12-27, is balanced on a seesaw. What is the number of the person who causes the largest torque about the rotation axis At fulcrum fdirected (a) out of the page and (b) into the page?

The masses of the people and distances between them.

Using the right-hand rule, you can find the direction of torque exerted by the people. Then using the formula for torque, you can find the magnitude of torques. After comparing them, you can decide which person exerts the maximum torque in each direction. The formula used is given below. $\tau =r\times F$

Using right hand rule, you note that the people marked 1 to 4 exert torques which are pointing out of the page, and the people marked 5 to 8 are pointing into the page.
The torques which are pointing out of the page are,
Torque exerting on person no.1:

$$\begin{gathered} {\tau }_1=220\left(4\right)\text{sin}90° \\ =880\text{Nm} \end{gathered}$$

Torque exerting on person no.2:

$$\begin{gathered} {\tau }_2=330\left(3\right)\text{sin}90° \\ {\tau }_1=990\text{Nm} \end{gathered}$$

Torque exerting on person no.3:

$$\begin{gathered} {\tau }_3=440\left(2\right)\text{sin}90° \\ =880\text{Nm} \end{gathered}$$

Torque exerting on person no.4:

$$\begin{gathered} {\tau }_4=560\left(1\right)\text{sin}90° \\ =560\text{Nm} \end{gathered}$$

Therefore, person no.2 causes the largest torque which is directing out of page about the rotation axis at fulcrum f.

Torque exerting on person no.5:

$$\begin{gathered} {\tau }_5=560\left(1\right)\text{sin}90° \\ =560\text{Nm} \end{gathered}$$

Torque exerting on person no.6:

$$\begin{gathered} {\tau }_6=440\left(2\right)\text{sin}90° \\ {\tau }_1=880\text{Nm} \end{gathered}$$

Torque exerting on person no.7:

$$\begin{gathered} {\tau }_7=330\left(3\right)\text{sin}90° \\ {\tau }_3=990\text{Nm} \end{gathered}$$

Torque exerting on person no.8:

$$\begin{gathered} {\tau }_8=220\left(4\right)\text{sin}90° \\ {\tau }_4=880\text{Nm} \end{gathered}$$

Therefore, the seventh person causes the largest torque which is directing out of page about the rotation axis at fulcrum f.