Let's solve each vector operation step by step using the given vectors:
Given:
- $ \mathbf{q} = \langle 2, -3 \rangle $
- $ \mathbf{t} = \langle -2, 3 \rangle $
- $ \mathbf{u} = \langle 5, -4 \rangle $
---
1. $ \mathbf{q} + \mathbf{t} $
Step: Add corresponding components:
$$
\langle 2 + (-2),\ -3 + 3 \rangle
$$
Answer:
$$
\langle 0,\ 0 \rangle
$$
---
2. $ \mathbf{q} + \mathbf{q} $
Step: Add $ \mathbf{q} $ to itself:
$$
\langle 2 + 2,\ -3 + (-3) \rangle
$$
Answer:
$$
\langle 4,\ -6 \rangle
$$
---
3. $ \mathbf{q} - \mathbf{u} $
Step: Subtract corresponding components:
$$
\langle 2 - 5,\ -3 - (-4) \rangle = \langle 2 - 5,\ -3 + 4 \rangle
$$
Answer:
$$
\langle -3,\ 1 \rangle
$$
---
4. $ \mathbf{t} - \mathbf{t} $
Step: Subtract $ \mathbf{t} $ from itself:
$$
\langle -2 - (-2),\ 3 - 3 \rangle = \langle -2 + 2,\ 3 - 3 \rangle
$$
Answer:
$$
\langle 0,\ 0 \rangle
$$
---
✔ Final Answers:
1. $ \mathbf{q} + \mathbf{t} $
Step => $ \langle 2 + (-2),\ -3 + 3 \rangle $
Answer => $ \langle 0,\ 0 \rangle $
2. $ \mathbf{q} + \mathbf{q} $
Step => $ \langle 2 + 2,\ -3 + (-3) \rangle $
Answer => $ \langle 4,\ -6 \rangle $
3. $ \mathbf{q} - \mathbf{u} $
Step => $ \langle 2 - 5,\ -3 - (-4) \rangle $
Answer => $ \langle -3,\ 1 \rangle $
4. $ \mathbf{t} - \mathbf{t} $
Step => $ \langle -2 - (-2),\ 3 - 3 \rangle $
Answer => $ \langle 0,\ 0 \rangle $
---
✔ Explanation Summary:
- Vector addition/subtraction is done component-wise.
- Adding a vector to its negative gives the zero vector.
- Doubling a vector means doubling each component.
- Subtracting a vector from itself always results in the zero vector.
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Parent Tip: Review the logic above to help your child master the concept of subtracting vectors worksheet.
