In this worksheet, we will practice finding the angle between two vectors in space using their dot product.

**Q2: **

Given , , , and , determine the measure of the angle between vectors and rounded to the nearest hundredth.

**Q3: **

Find .

- A0
- B
- C1
- D
- E

**Q4: **

If and , find the measure of the angle between the two vectors rounded to the nearest hundredth.

**Q5: **

Given that and , determine, to the nearest hundredth, the measure of the smaller angle between the two vectors.

**Q6: **

Given that , , and , determine the measure of the smaller angle between the two vectors.

**Q7: **

The angle between and is . If , find to the nearest hundredth.

**Q8: **

Find the angle between the vectors and . Give your answer correct to two decimal places.

**Q9: **

Find the angle between the vectors and . Give your answer correct to two decimal places.

**Q10: **

Find the angle between the vectors and .

**Q11: **

Find the angle between the vectors and .

**Q12: **

Find the angle between the vectors and .

**Q13: **

Find the angle between the vectors and . Give your answer correct to one decimal place.

**Q14: **

Find the value of given , and where is the angle between the vectors and . Give the answer to two decimal places.

**Q15: **

Given that and , determine, to the nearest hundredth, the measure of the smaller angle between the two vectors.

**Q16: **

Given , , , and , determine the measure of the angle between vectors and rounded to the nearest hundredth.

**Q17: **

Given , , , and , determine the measure of the angle between vectors and rounded to the nearest hundredth.

**Q18: **

If and , find the measure of the angle between the two vectors rounded to the nearest hundredth.