# 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.

Q1:

Given that and , find .

• A
• B
• C
• D

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 ?

• 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

Q21:

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

• A
• B
• CThey are both the same.

Q22:

Find all the possible values of given , and .

• A,
• B
• C18, 6
• D1

Q23:

Given that and , find .

• A
• B
• C
• D

Q24:

Given that and , find .

• A
• B
• C
• D

Q25:

Given that and , find .

• A
• B
• C
• D