In this example, we are given vectors u, v, and w, and we're asked to sketch the resultant vector u plus v minus w. So let's see how we can do this. Now, what I'm first going to do is I'm going to rewrite this operation over here. So we're going to have u, but rather than having v minus w in the parenthesis, I'm going to write this as v plus negative w. This will just allow us to see what our vectors are going to look like on this grid. Now, I'm first going to deal with what's inside the parentheses and I'm going to find negative w. Now, I can see that vector w is right there and if I negate w, it's going to have the same magnitude but opposite direction. So we're going to start here and we're going to finish over there because it's going to be pointing in the opposite direction as w. So this would be vector negative w.

So now that we found negative w, the next thing I'm going to deal with is finding v plus negative w. And I can do this using the tip-to-tail method. So I can see that the tip of vector 'v' is right there and the tail of vector 'negative w' is right here. So if I go ahead and move negative 'w' up there I can connect these tip to tail and I can see that vector negative 'w' is 1, 2, 3, 4, 5, 6 units to the left. So starting here we're going to go 1, 2, 3, 4, 5, 6 units to the left and this right here is vector negative w. Now to find vector v plus negative w I can just draw the resultant vectors. The resultant vector will start here, finish there and that is going to be the vector v plus negative w, which is also v minus w, it's okay to write it like that as well, so this is what we end up getting.

Now from here, what I need to do next, is find vector u plus v minus w. We already figured out this is vector v minus w, so what I'm going to do is use the tip-to-tail method on this vector. So we'll have the tip of vector u connected to the tail of vector v minus w. So I'll write the v minus w vector right there and I see that this vector is 1, 2, 3 units to the left and 2 units down so we'll go 1, 2, 3 units to the left and 2 units down and that's going to be vector v minus w and I'll put this in parentheses just to match what we have in the problem and then all I need to do is draw another resultant vector which is going to go from the initial point of u to the final point or terminal point of v minus w and that's going to give me the vector u plus v minus w and that right there is the vector and the solution to this problem. So, I hope you found this video helpful. Thanks for watching.