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

**Q2: **

Given that and , find the possible values of .

- A
- B12
- C
- D

**Q3: **

Given that and , find .

- A
- B
- C
- D

**Q4: **

A force of newtons is being applied to an object. What other force should be applied to achieve a total force of newtons?

- A newtons
- B newtons
- C newtons
- D newtons
- E newtons

**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

**Q17: **

Given that and , express in terms of and .

- A
- B
- C
- D

**Q18: **

If , , and , express in terms of and .

- A
- B
- C
- D

**Q19: **

When is it true that ?

- Aonly when and are parallel
- Bonly when and are equivalent
- Conly when and are perpendicular
- Dfor any vectors and
- Eonly when and are not perpendicular

**Q20: **

When is it true that ?

- Anever
- Balways
- Cwhen and are equivalent vectors
- Dwhen and are parallel vectors
- Ewhen and are perpendicular vectors

**Q21: **

and are two vectors, where and . Comparing and , which quantity is larger?

- AThey are both the same.
- B
- C

**Q22: **

Find all the possible values of given , and .

- A
- B1
- C ,
- D18, 6