# 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 is a square of side 33, determine .

Q8:

Find .

Q9:

Given that and , determine .

Q10:

If and are two perpendicular unit vectors, find .

Q11:

Which of the following is true of the vectors and ?

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

Q12:

If and , calculate .

Q13:

If and , find .

Q14:

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

Q15:

If , , and , find the value of .

• A
• B
• C
• D

Q16:

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

Q17:

For the unit vectors , , , what is ?

Q18:

For the unit vectors , , , what is ?

Q19:

and are two vectors, where and . Is ? Justify your answer.

• AYes because .
• BNo because .
• CNo because .
• DYes because .

Q20:

If and , find .

Q21:

Let and . Calculate .

Q22:

If , , and , find .

• A
• B
• C
• D

Q23:

For the unit vectors , , , what is ?

Q24:

Given that and , determine .

Q25:

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