# Worksheet: Dot Product in 3D

In this worksheet, we will practice finding the dot product of two vectors in 3D.

Q1:

If and are two perpendicular vectors, then .

Q2:

If the dot product of two nonzero vectors is zero, what does this tell us about the two vectors?

• AThe two vectors are equal in magnitude but opposite in direction.
• BThey are parallel in opposite directions.
• CThey are perpendicular.
• DIt does not indicate anything about the two vectors.
• EThey are parallel in the same direction.

Q3:

For the unit vectors , , , what is ?

Q4:

Given that and , determine .

Q5:

Given that the coordinates of , , and are , , and , respectively, determine .

Q6:

For what value of are vectors and perpendicular?

• A
• B
• C
• D

Q7:

Given that and , determine .

Q8:

If and are two perpendicular unit vectors, find .

Q9:

Which of the following is true of the vectors and ?

• AThey are perpendicular.
• BThey are neither parallel nor perpendicular.
• CThey are parallel.

Q10:

If and , find .

Q11:

Given that , , , and is perpendicular to the vector , determine .

Q12:

If , , and , find the value of .

• A
• B
• C
• D

Q13:

Determine , given that the scalar product of the two vectors and is 27.

Q14:

For the unit vectors , , , what is ?

Q15:

For the unit vectors , , , what is ?

Q16:

If and , find .

Q17:

If , , and , find .

• A
• B
• C
• D

Q18:

For the unit vectors , , , what is ?

Q19:

Given that and , determine .

Q20:

Suppose , , and the angle between the two vector is . Find to the nearest hundredth.

Q21:

Given that , , , , , and , determine .

• A
• B
• C
• D

Q22:

Given that and are two unit vectors, and , evaluate .

Q23:

For the unit vectors , , , what is ?

Q24:

For the unit vectors , , , what is ?

Q25:

If and are unit vectors, which interval does lie in?

• A
• B
• C
• D