# Worksheet: Adding and Subtracting Vectors in 2D

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

Q1:

Given that and , find .

• A
• B
• C
• D
• E

Q2:

Given that , , and , find .

• A
• B
• C
• D
• E

Q3:

Given that , , and , find .

• A
• B
• C
• D

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

Q19:

Fill in the blank: If is a vector in a plane, then the vector .

• Ais perpendicular to
• Bmakes an angle of with and is twice as long
• Cmakes an angle of with
• Dmakes an angle of 0 with and is twice as long

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

Q23:

Does the vector sum have a solution?

• 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,