# Worksheet: Angle between Two Vectors in Space

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

Q1:

If , , and , where is a unit vector, find the measure of the angle between and rounded to the nearest minute given .

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Q2:

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

Q3:

Find .

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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.

Q19:

Determine the angle between the vectors and in .

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• C0
• D