# Worksheet: The Angle between Two Vectors in the Coordinate Plane

In this worksheet, we will practice using the dot product to find the angle between two nonzero vectors in a plane.

**Q3: **

Suppose a rectangle with and . Determine .

**Q4: **

Find the value of approximated to the nearest hundredth.

**Q5: **

.

- A
- B
- C
- D
- E

**Q6: **

If and satisfy , how are the two vectors related?

- Aperpendicular
- Bparallel

**Q7: **

Suppose square of side 32.6. Determine .

**Q8: **

In a rectangle , and . Determine .

**Q9: **

If is a regular hexagon whose side is 7.1, find .

**Q10: **

If is a regular hexagon whose side is 9.6, find .

**Q11: **

Triangle has a right angle at . Given , , and that is the midpoint of . Determine to the nearest hundredth.

**Q12: **

Triangle has a right angle at . Given , , and that is the midpoint of , determine to the nearest hundredth.

**Q13: **

Triangle has a right angle at . Given and , determine .

**Q14: **

If and , find all the possible values of that make the measure of the angle between the two vectors .

- A or
- B or
- C or
- D or

**Q15: **

Let and Find the angle between and giving your answer to two decimal places.

**Q16: **

Given that , and , determine the angle between the two vectors rounded to the nearest minute.

- A
- B
- C
- D

**Q17: **

If , and is the angle between and , find the value of in the range .

**Q18: **

If , , and the measure of the angle between and is , calculate .

- A
- B
- C
- D80
- E

**Q19: **

If , find the value of in the range ,where is the angle between and .

**Q20: **

If is the angle between and and , find the value of in the range .

**Q21: **

Given that , , and the measure of the angle between and is , determine to the nearest hundredth.

**Q22: **

Between unit vectors and is an angle of . Find to the nearest tenth.

**Q23: **

If is the smaller angle between the two vectors and , find .

- A
- B
- C
- D
- E

**Q24: **

Given that , , and , determine the measure of the angle between and rounded to the nearest minute.

- A
- B
- C
- D

**Q25: **

Given that , , and , determine , and give the measure of the angle between and to the nearest hundredth.

- A ,
- B ,
- C ,
- D ,