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 .

  • A
  • B
  • C
  • D
  • E

Q2:

Given 𝐴 ( 3 , 5 , 6 ) , 𝐵 ( 0 , 3 , 7 ) , 𝐶 ( 8 , 1 0 , 2 ) , and 𝐷 ( 3 , 9 , 6 ) , determine the measure of the angle between vectors 𝐴 𝐵 and 𝐶 𝐷 rounded to the nearest hundredth.

Q3:

Find 𝐴 × 𝐵 𝐴 𝐵 .

  • A0
  • B s i n 𝜃
  • C1
  • D t a n 𝜃
  • E c o s 𝜃

Q4:

If 𝐴 = 2 𝑖 + 5 𝑘 and 𝐵 = 4 𝑖 + 3 𝑗 + 𝑘 , find the measure of the angle between the two vectors rounded to the nearest hundredth.

Q5:

Given that 𝐴 = 4 𝑖 𝑗 2 𝑘 and 𝐵 = ( 2 , 2 , 4 ) , determine, to the nearest hundredth, the measure of the smaller angle between the two vectors.

Q6:

Given that 𝐴 = 3 5 , 𝐵 = 2 3 , and 𝐴 𝐵 = 8 0 5 2 2 , determine the measure of the smaller angle between the two vectors.

Q7:

The angle between 𝐴 and 𝐵 is 2 2 . If 𝐴 = 3 𝐵 = 2 5 . 2 , find 𝐴 𝐵 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 𝑥 given 𝐴 = 4 𝜃 , 𝑥 , 𝜃 c o s l o g s i n 3 , 𝐵 = 𝜃 , 1 6 , 4 𝜃 c o s l o g s i n 2 and 𝐴 𝐵 = 1 0 where 𝜃 is the angle between the vectors 𝐴 and 𝐵 . Give the answer to two decimal places.

Q15:

Given that 𝐴 = 4 𝑖 + 7 𝑗 + 6 𝑘 and 𝐵 = ( 1 , 4 , 2 ) , determine, to the nearest hundredth, the measure of the smaller angle between the two vectors.

Q16:

Given 𝐴 ( 7 , 4 , 0 ) , 𝐵 ( 7 , 1 , 9 ) , 𝐶 ( 4 , 5 , 8 ) , and 𝐷 ( 1 , 6 , 4 ) , determine the measure of the angle between vectors 𝐴 𝐵 and 𝐶 𝐷 rounded to the nearest hundredth.

Q17:

Given 𝐴 ( 6 , 9 , 1 0 ) , 𝐵 ( 0 , 5 , 6 ) , 𝐶 ( 1 0 , 1 0 , 4 ) , and 𝐷 ( 7 , 6 , 2 ) , determine the measure of the angle between vectors 𝐴 𝐵 and 𝐶 𝐷 rounded to the nearest hundredth.

Q18:

If 𝐴 = 7 𝑖 + 2 𝑗 + 4 𝑘 and 𝐵 = 5 𝑖 + 𝑘 , find the measure of the angle between the two vectors rounded to the nearest hundredth.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.