In this worksheet, we will practice calculating the vector product of two vectors and using the vector product to find the angle between two vectors.

**Q2: **

For the vectors shown in the accompanying diagram, the positive -axis corresponds to horizontally right and the positive -axis corresponds to vertically upwards.

Find the component of vector along vector .

- A7.13
- B6.46
- C8.49
- D8.66
- E9.12

Find the component of vector along vector .

- A10.4
- B11.0
- C9.35
- D8.73
- E10.1

Find the component of vector along vector .

- A0.909
- B0.708
- C0.866
- D0.783
- E0.810

Find the component of vector along vector .

- A17.3
- B18.0
- C16.8
- D13.8
- E15.1

**Q3: **

Consider the vectors and .

Find .

- A
- B
- C
- D
- E

Find .

Find the angle between and .

Find the angle between and .

**Q4: **

A convoy of vehicles has a velocity vector .

What is the unit vector of the convoy’s direction of motion?

- A
- B
- C
- D
- E

At what angle north of east does the convoy move?

**Q5: **

The positive -axis is horizontal to the right for the vectors shown.

What is the vector product ?

- A
- B
- C
- D
- E

What is the vector product ?

- A
- B
- C
- D
- E

What is the vector product ?

- A
- B
- C
- D
- E

What is the vector product ?

- A
- B
- C
- D
- E

What is the vector product ?

- A
- B
- C
- D
- E

What is the vector product ?

- A
- B
- C
- D
- E

What is the vector product ?

- A
- B
- C
- D
- E

**Q6: **

Calculate the product .

- A
- B
- C
- D
- E

**Q7: **

Three dogs pull on a stick, all in different directions, exerting forces , , and . N, N, and N. The forces , , and apply the displacement vector cm to the stick.

What is the angle between and ?

What magnitude of work is done by ?

What magnitude of work is done by ?

**Q8: **

Calculate the product .

**Q9: **

Calculate the product .

**Q10: **

Find the angle between the two vectors and .

**Q11: **

What is the relationship between the directions of two vectors for which the dot product is zero?

- AThey are coplanar.
- BThey are parallel.
- CThey form a 45 degrees angle with respect to one another.
- DThey are perpendicular (orthogonal).
- EThey are antiparallel.

**Q12: **

Calculate the dot product of and . Which of the following matches the result?

- A16
- B12
- C72
- D44
- E38

**Q13: **

Calculate the cross product of and . Which of the following best matches the result?

- A
- B
- C
- D
- E

**Q14: **

Which of the following is closest to the angle between the two vectors and ?

- A 70 degrees
- B 55 degrees
- C 32 degrees
- D 50 degrees
- E 5 degrees

**Q15: **

Two displacement vectors and have magnitudes of 10.0 m and 20.0 m respectively. The directions of and make counterclockwise angles of and ,respectively, with the positive -axis, as shown in the accompanying diagram. Find the product . Answer to three significant figures.