# Worksheet: Vector Operations in 2D

In this worksheet, we will practice performing operations on vectors algebraically such as vector addition, vector subtraction, and scalar multiplication in two dimensions.

**Q2: **

Given that and , find the possible values of .

- A
- B12
- C
- D

**Q3: **

Given that and , find .

- A
- B
- C
- D

**Q5: **

Given that and , find the components of .

- A
- B
- C
- D
- E

**Q6: **

Given that , , and , find the components of .

- A
- B
- C
- D
- E

**Q7: **

Given that , , and , find the components of .

- A
- B
- C
- D
- E

**Q8: **

Given that and , find the components of .

- A
- B
- C
- D
- E

**Q9: **

Shown on the grid of unit squares are the vectors , , and .

What are the components of ?

- A
- B
- C
- D
- E

What are the components of ?

- A
- B
- C
- D
- E

What are the components of ?

- A
- B
- C
- D
- E

**Q10: **

The figure shows a regular hexagon divided into 6 equilateral triangles. Which of the following is equal to ?

- A
- B
- C
- D
- E

**Q11: **

Given that and , find the components of .

- A
- B
- C
- D
- E

**Q12: **

Given that , and , find the components of .

- A
- B
- C
- D
- E

**Q13: **

Given that = and = find the components of + .

- A
- B
- C
- D
- E

**Q14: **

and Find .

**Q15: **

On a lattice, where , , and , determine the coordinates of the point .

- A
- B
- C
- D

**Q16: **

On a lattice, where , , and , find the coordinates of the point .

- A
- B
- C
- D
- E

**Q18: **

If , , and , express in terms of and .

- A
- B
- C
- D

**Q19: **

When is it true that ?

- Afor any vectors and
- Bonly when and are not perpendicular
- Conly when and are equivalent
- Donly when and are perpendicular
- Eonly when and are parallel

**Q20: **

When is it true that ?

- Aalways
- Bwhen and are perpendicular vectors
- Cnever
- Dwhen and are equivalent vectors
- Ewhen and are parallel vectors

**Q22: **

Find all the possible values of given , and .

- A,
- B
- C18, 6
- D1