# Worksheet: Dot Product in 3D

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

**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 ?

**Q6: **

For what value of are vectors and perpendicular?

- A
- B
- C
- D

**Q7: **

Given that is a square of side 33, determine .

**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.

**Q13: **

If and , find .

**Q14: **

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

- A
- B7
- C15
- D

**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 ?

**Q20: **

If and , find .

**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.