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 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.

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 ⃗ .

⟨ 6 , 4 ⟩ \langle6,4\rangle ⟨ 6 , 4 ⟩

⟨ 4 , 4 ⟩ \langle4,4\rangle ⟨ 4 , 4 ⟩

⟨ 5 , 4 ⟩ \langle5,4\rangle ⟨ 5 , 4 ⟩

⟨ 6 , 6 ⟩ \langle6,6\rangle ⟨ 6 , 6 ⟩

14. Vectors

Vectors in Component Form

Precalculus

14. Vectors

Vectors in Component Form

Struggling with Precalculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

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

$\langle4,4\rangle$

$\langle5,4\rangle$

$\langle6,6\rangle$

$\langle6,4\rangle$

Verified step by step guidance

Identify the components of each vector: v⃗ = ⟨2, 1⟩, u⃗ = ⟨3, 4⟩, and w⃗ = ⟨-1, 1⟩.

To find v⃗ + u⃗, add the corresponding components of vectors v⃗ and u⃗. This means adding the x-components and the y-components separately.

Calculate the sum of the x-components: 2 (from v⃗) + 3 (from u⃗) = 5.

Calculate the sum of the y-components: 1 (from v⃗) + 4 (from u⃗) = 5.

Now, subtract the components of w⃗ from the result of v⃗ + u⃗. Subtract the x-component of w⃗ from the x-component of the sum, and the y-component of w⃗ from the y-component of the sum. This results in ⟨5 - (-1), 5 - 1⟩.

3:55m

Watch next

Master Position Vectors & Component Form with a bite sized video explanation from Patrick

Start learning

Vectors in Component Form practice set

Problem sets built by lead tutors

Expert video explanations

Go to Practice