If vectors v⃗=⟨2,1⟩v ⃗=⟨2,1⟩v⃗=⟨2,1⟩, u⃗=⟨3,4⟩u ⃗=⟨3,4⟩u⃗=⟨3,4⟩, and w⃗=⟨−1,1⟩w ⃗=⟨-1,1⟩w⃗=⟨−1,1⟩, calculate v⃗+u⃗−w⃗v ⃗+u ⃗-w ⃗v⃗+u⃗−w⃗.

⟨ 6 , 4 ⟩ \langle6,4\rangle ⟨ 6 , 4 ⟩

If vectors v ⃗ = ⟨ 2 , 1 ⟩ v ⃗=⟨2,1⟩ v ⃗ = ⟨ 2 , 1 ⟩ , u ⃗ = ⟨ 3 , 4 ⟩ u ⃗=⟨3,4⟩ u ⃗ = ⟨ 3 , 4 ⟩ , and w ⃗ = ⟨ − 1 , 1 ⟩ w ⃗=⟨-1,1⟩ w ⃗ = ⟨ − 1 , 1 ⟩ , calculate v ⃗ + u ⃗ − w ⃗ v ⃗+u ⃗-w ⃗ v ⃗ + u ⃗ − w ⃗ .

Welcome back, everyone. So let's give this problem a try. So in this problem, we have these 3 vectors. We have v is equal to 21. We have u is equal to 34, and then we have w is equal to negative 11. And we want to calculate this operation, v plus u minus w. Now the first thing I'm going to do is I'm going to take this by the steps. So I'm going to first figure out what u minus w is equal to, and then I'll add the vector v onto it. Now to calculate u minus w, I can go to the vectors we have up here. I see that u is equal to 34, and then I see that w is equal to negative 11. Now this operation says we need to subtract these 2 vectors, so I'm going to subtract them. Now when adding or subtracting vectors, you just want to add or subtract the corresponding components. So I can subtract these x values here, which is 3 minus negative one. 3 minuteus negative one is the same thing as 3 plus 1 which is 4. So we're going to have 4 comma and then we're going to subtract the y values. Now the y values are gonna be 4 minus 1 for these components here, which means that we're going to end up with a total y value here of 3. So our vector is 43 when we subtract u and w. So now that we've gone ahead and found this vector, I can now implement this plus v. So we figured out what u minus w is, but now we need to figure out what v plus u minus w is. Well, if we have u minus w and we have v, we can just add the vectors we see. So we can see that v here is 21. And then what I can do is add 21 to u minus w, which is the vector that we just calculated for 3. So I have 21 plus 43, and we'll have 2 plus 4 which is 6, and then we'll have 3 or excuse me 1 plus 3 which is 4. So we're going to end up with 64. So the vector v plus u minus w comes out to 6 4. So this right here is our vector and the solution to this problem. So hope you found this video helpful. Thanks for watching.