### Video Transcript

A body was moving uniformly under the effect of three forces ๐น one, ๐น two, and ๐น three. Given that ๐น one equals seven ๐ and ๐น two equals eight ๐, where ๐ and ๐ are orthogonal unit vectors, determine ๐น three which ensures that it will move at a constant velocity.

Weโre told in this statement two forces that are acting on a body, ๐น one and ๐น two, as well as their force descriptors. We want to solve for the value of the third force, ๐น 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 ๐น three, letโs recall Newtonโs second law of motion. Newtonโs 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, weโre 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 โ ๐น one, ๐น two, and ๐น three โ is equal to ๐ times ๐ which equals zero.

If we replace ๐น one and ๐น two with their component expressions and then subtract those components from both sides of our equation, we see that ๐น three equals negative seven ๐ minus eight ๐. Thatโs what ๐น three must be in order for the net force on our object to be zero.