# Worksheet: Adding and Subtracting Vectors in 2D

In this worksheet, we will practice adding and subtracting vectors in 2D.

**Q4: **

Given that and , find .

- A
- B
- C
- D
- E

**Q5: **

A woman started walking from home and walked 6 miles at north of east, then 2 miles at east of south, then 5 miles at south of west. If she walked straight home, how far would she have to walk and in what direction? Give the distance in miles correct to 2 decimal places and the direction in degrees correct to one decimal place.

- A1.93 miles, east of north
- B6.06 miles, north of west
- C0.97 miles, north of west
- D1.93 miles, west of north
- E6.06 miles, west of north

**Q6: **

Given that , , and , determine the vector that satisfies the equation .

- A
- B
- C
- D

**Q7: **

Given that and , find .

- A
- B
- C
- D

**Q8: **

If and , what is the smallest that could be?

**Q9: **

Are there any vector and for which ?

- Ano
- Byes

**Q10: **

Let and .

What are the components of ?

- A
- B
- C
- D
- E

What are the components of ?

- A
- B
- C
- D
- E

**Q11: **

Consider the vectors and .

What is the magnitude of ? Give your answer correct to two decimal places if needed.

What is the magnitude of ? Give your answer correct to two decimal places if needed.

What is the magnitude of ? Give your answer correct to two decimal if needed.

**Q12: **

Consider the vectors and .

What is the magnitude of ? Give your answer correct to two decimal places if needed.

What is the magnitude of ? Give your answer correct to two decimal places if needed.

What is the magnitude of ? Give your answer correct to two decimal places if needed.

**Q13: **

Given that and , where and are two perpendicular unit vectors, find .

- A
- B
- C
- D
- E

**Q14: **

Given that and , where and are two perpendicular unit vectors, find .

- A
- B2
- C4
- D
- E

**Q15: **

Given that , and , find .

- A
- B
- C
- D

**Q16: **

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

**Q17: **

If , and , determine .

- A
- B
- C
- D

**Q18: **

A woman started walking from home and walked 4 miles east, 7 miles southeast, 6 miles south, 5 miles southwest, and 3 miles east. How far did she walk in total? If she walked in a straight line back home, how far would she have to walk? Give your answer correct to three decimal places if necessary.

- A25 miles, 16.752 miles
- B15 miles, 16.752 miles
- C25 miles, 21.204 miles
- D15 miles, 21.204 miles
- E9 miles, 12.727 miles

**Q20: **

Let be the zero vector. What is equal to for any vector ?

- A
- B

**Q21: **

Is it always true that ?

- Ayes
- Bno

**Q22: **

Is it always true that ?

- ANo
- BYes

**Q24: **

Let be the zero vector. What is equal to for any vector ?

- A
- B

**Q25: **

Given that , find the values of and .

- A,
- B,
- C,
- D,