CP 2.2

Professor: Using vectors v and w given in the image below, sketch the vector 2w minus v. We have two vectors given to us. Vector v has an initial point, and it goes up and to the right at a certain distance. That'll be its magnitude. And we have the vector w, which goes down and to the right with a certain magnitude. 

So in order to sketch 2w minus v, we first need to imagine what the vector w would look like and find twice that magnitude. So I'm going to draw a vector. I'm just going to pick an initial point here and go down to the right, twice the distance of w. So this would be my vector down to the right of 2w. 

Now, beginning at the terminal point of that vector, I'm going to add on to this a minus v vector, which would be the vector v, same magnitude, but in the opposite direction. So this would be going down and to the left. So beginning at the tail of 2w, I'm going to go down to the left, that same distance, that same magnitude. Now the vector 2w minus v will begin where 2w began, that initial point, and it will end at the terminal point of minus v. And that is our vector.