# Worksheet: Dot Product in 3D

Q1:

Given that and , determine .

Q2:

Given that and , determine .

Q3:

Given that and , determine .

Q4:

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

Q5:

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

Q6:

If and are two perpendicular vectors, then .

Q7:

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

• AThey are parallel in opposite directions.
• BThey are parallel in the same direction.
• CIt does not indicate anything about the two vectors.
• DThey are perpendicular.
• EThe two vectors are equal in magnitude but opposite in direction.

Q8:

If and , calculate .

Q9:

Find .

Q10:

and Find .

Q11:

If and , find .

Q12:

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

• A7
• B
• C15
• D

Q13:

If , , and , find the value of .

• A
• B
• C
• D

Q14:

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

Q15:

For the unit vectors , , , what is ?

Q16:

For the unit vectors , , , what is ?

Q17:

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

• AYes because .
• BYes because .
• CNo because .
• DNo because .

Q18:

If and , find .

Q19:

Decide which relation holds between the vectors and .

• Aperpendicular
• Bparallel
• Cotherwise

Q20:

Decide which relation holds between the vectors and .

• Aotherwise
• Bperpendicular
• Cparallel

Q21:

Decide which relation holds between the vectors and .

• Aotherwise
• Bperpendicular
• Cparallel

Q22:

Decide which relation holds between the vectors and .

• Aotherwise
• Bperpendicular
• Cparallel

Q23:

Given that and , determine .

Q24:

For the unit vectors , , , what is ?

Q25:

Let and . Calculate .