# Lesson Worksheet: Vector Operations in 3D Mathematics

In this worksheet, we will practice doing operations on vectors in 3D, such as addition, subtraction, and scalar multiplication.

Q1:

If and , find .

• A
• B
• C
• D

Q2:

If and , find .

• A
• B
• C

Q3:

If , and , determine the vector for which .

• A
• B
• C
• D

Q4:

If and , find .

• A
• B
• C
• D

Q5:

If , , and , find .

• A
• B
• C
• D
• E

Q6:

If , , and , find .

• A1
• B2
• C
• D
• E

Q7:

Suppose that , , and . What is ?

• A
• B
• C
• D

Q8:

Given that and that is a unit vector equal to , determine the possible values of .

• A
• B
• C
• D

Q9:

Suppose a unit vector is such that . Determine the possible values of .

• A
• B
• C
• D

Q10:

Given and , determine the unit vector in the direction .

• A
• B
• C
• D

Q11:

Find the unit vector in the direction of , where and .

• A
• B
• C
• D

Q12:

Find so that the points , , are collinear.

Q13:

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

• AThey are both the same.
• B
• C

Q14:

Given the two vectors and , find .

• A
• B
• C
• D
• E

Q15:

If and , find .

• A
• B
• C
• D
• E

Q16:

Given that and , find .

• A
• B3
• C
• D9
• E

Q17:

If and , find .

• A
• B
• C
• D
• E

Q18:

True or False: If and , then .

• AFalse
• BTrue

Q19:

True or False: Given that , , and , then .

• ATrue
• BFalse

Q20:

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

• A
• B
• C
• D
• E

Q21:

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

Q22:

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

• A
• B
• CThey are both the same.

Q23:

Given that and , find the following.

• A
• B
• C
• D
• E

, where is a constant

• A
• B
• C
• D
• E

• A
• B
• C
• D
• E

Q24:

If and , find .

• A
• B
• C
• D
• E

Q25:

True or False: If is any vector in 3D and is the zero vector, then, for any vector , equals .

• ATrue
• BFalse