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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:

Find the angle πœƒ between the vectors V = ⟨ 5 , 1 , βˆ’ 2 ⟩ and W = ⟨ 4 , βˆ’ 4 , 3 ⟩ . Give your answer correct to two decimal places.

Q3:

The angle between A and B is 2 2 ∘ . If | | = 3 | | = 2 5 . 2 A B , find A B β‹… to the nearest hundredth.

Q4:

Find .

  • A0
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  • C1
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  • E

Q5:

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

Q6:

Find the angle πœƒ between the vectors V = ⟨ 2 , 1 , 4 ⟩ and W = ⟨ 1 , βˆ’ 2 , 0 ⟩ .

Q7:

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

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Q8:

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

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  • D

Q9:

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

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  • D

Q10:

Given , , , and , determine the size of the angle between vectors and approximated to the nearest hundredth.

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  • D

Q11:

Given , , , and , determine the size of the angle between vectors and approximated to the nearest hundredth.

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  • D

Q12:

Given , , , and , determine the size of the angle between vectors and approximated to the nearest hundredth.

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  • B
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  • D

Q13:

If and , find the size of the angle between the two vectors approximated to the nearest hundredth.

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  • B
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  • D

Q14:

If and , find the size of the angle between the two vectors approximated to the nearest hundredth.

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  • D

Q15:

Find the angle πœƒ between the vectors V = ⟨ 4 , 2 , βˆ’ 1 ⟩ and W = ⟨ 8 , 4 , βˆ’ 2 ⟩ .

Q16:

Find the value of π‘₯ given A =  4 πœƒ , π‘₯ , πœƒ  c o s l o g s i n 3 , B =  πœƒ , 1 6 , 4 πœƒ  c o s l o g s i n 2 and A B β‹… = 1 0 where πœƒ is the angle between the vectors A and B . Give the answer to two decimal places.

Q17:

Find the angle πœƒ between the vectors V i j k = βˆ’ + 2 + and W i j k = βˆ’ 3 + 6 + 3 .

Q18:

Find the angle πœƒ between the vectors V = ⟨ 7 , 2 , βˆ’ 1 0 ⟩ and W = ⟨ 2 , 6 , 4 ⟩ . Give your answer correct to one decimal place.

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