### Video Transcript

A body was moving uniformly under the effect of three forces πΉ one, πΉ two, and πΉ three. Given that πΉ one equals seven π and πΉ two equals eight π, where π and π are orthogonal unit vectors, determine πΉ three which ensures that it will move at a constant velocity.

Weβre told in this statement two forces that are acting on a body, πΉ one and πΉ two, as well as their force descriptors. We want to solve for the value of the third force, πΉ three, which ensures that, overall, the body will move at a constant velocity. In other words, that its acceleration will be zero.

To start solving for πΉ three, letβs recall Newtonβs second law of motion. Newtonβs second law says that the net force acting on an object is equal to the mass of that object times its acceleration. In our scenario, weβre told the object moves at a constant velocity. That means that its acceleration is zero. So we can write, the sum of our three forces β πΉ one, πΉ two, and πΉ three β is equal to π times π which equals zero.

If we replace πΉ one and πΉ two with their component expressions and then subtract those components from both sides of our equation, we see that πΉ three equals negative seven π minus eight π. Thatβs what πΉ three must be in order for the net force on our object to be zero.