### Video Transcript

Complete the following. If the couples π sub one and π sub two are in equilibrium, where π sub one minus π sub two is equal to five π€, then π sub one plus π sub two is equal to what.

In this question, we are given two pieces of information about the couples π sub one and π sub two. Firstly, theyβre in equilibrium, and secondly π sub one minus π sub two is equal to five π€. We recall that a couple is a pair of parallel but not coincident forces of equal magnitudes and opposite directions. Also, if couples are in equilibrium, as in this case, the counterclockwise moment due to the couples equals the clockwise moment due to the couples. This means that for our two couples, π sub one and π sub two, π sub one must be equal to negative π sub two. And rearranging this equation gives us π sub one plus π sub two is equal to zero.

Since the difference between the couples was given in terms of the unit vector π€, we can also write the sum of the couples in this form. π sub one plus π sub two is equal to zero π€.