In this worksheet, we will practice finding the dot product of two vectors and deducing whether they are perpendicular, parallel, or intersecting.

**Q2: **

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.

**Q3: **

For the unit vectors , , , what is ?

**Q4: **

and Find .

**Q7: **

For what value of are vectors and perpendicular?

- A
- B
- C
- D

**Q8: **

Given that is a square of side 33, determine .

**Q9: **

Find .

**Q10: **

Given that and , determine .

**Q11: **

If and are two perpendicular unit vectors, find .

**Q12: **

Which of the following is true of the vectors and ?

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

**Q13: **

If and , calculate .

**Q14: **

If and , find .

**Q15: **

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

- A7
- B
- C15
- D

**Q16: **

If , , and , find the value of .

- A
- B
- C
- D

**Q17: **

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

**Q18: **

For the unit vectors , , , what is ?

**Q19: **

For the unit vectors , , , what is ?

**Q20: **

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

- AYes because .
- BYes because .
- CNo because .
- DNo because .

**Q21: **

If and , find .

**Q22: **

Let and . Calculate .

**Q23: **

If , , and , find .

- A
- B
- C
- D

**Q24: **

For the unit vectors , , , what is ?

**Q25: **

Given that and , determine .