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 ||=9.5A, ||=15.0B, and ABC×=122, where C is a unit vector, find the measure of the angle 𝜃 between A and B rounded to the nearest minute given 0<𝜃<90.

  • A 3 7 3 3
  • B 5 8 5 3
  • C 5 2 4 3
  • D 3 1 7
  • E 1 2 1 7

Q2:

Given 𝐴(3,5,6), 𝐵(0,3,7), 𝐶(8,10,2), and 𝐷(3,9,6), determine the measure of the angle between vectors 𝐴𝐵 and 𝐶𝐷 rounded to the nearest hundredth.

Q3:

Find |×|ABAB.

  • A t a n 𝜃
  • B s i n 𝜃
  • C0
  • D1
  • E c o s 𝜃

Q4:

If Aik=2+5 and Bijk=4+3+, find the measure of the angle between the two vectors rounded to the nearest hundredth.

Q5:

Given that Aijk=42 and B=2,2,4, determine, to the nearest hundredth, the measure of the smaller angle between the two vectors.

Q6:

Given that ||=35A, ||=23B, and AB=80522, determine the measure of the smaller angle between the two vectors.

Q7:

The angle between A and B is 22. If ||=3||=25.2AB, find AB to the nearest hundredth.

Q8:

Find the angle 𝜃 between the vectors V=5,1,2 and W=4,4,3. Give your answer correct to two decimal places.

Q9:

Find the angle 𝜃 between the vectors Vi= and Wijk=3+2+4. Give your answer correct to two decimal places.

Q10:

Find the angle 𝜃 between the vectors V=2,1,4 and W=1,2,0.

Q11:

Find the angle 𝜃 between the vectors V=4,2,1 and W=8,4,2.

Q12:

Find the angle 𝜃 between the vectors Vijk=+2+ and Wijk=3+6+3.

Q13:

Find the angle 𝜃 between the vectors V=7,2,10 and W=2,6,4. Give your answer correct to one decimal place.

Q14:

Find the value of 𝑥 given A=4𝜃,𝑥,𝜃coslogsin, B=𝜃,16,4𝜃coslogsin and AB=10 where 𝜃 is the angle between the vectors A and B. Give the answer to two decimal places.

Q15:

Given that Aijk=4+7+6 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 𝐴𝐵 and 𝐶𝐷 rounded to the nearest hundredth.

Q17:

Given 𝐴(6,9,10), 𝐵(0,5,6), 𝐶(10,10,4), and 𝐷(7,6,2), determine the measure of the angle between vectors 𝐴𝐵 and 𝐶𝐷 rounded to the nearest hundredth.

Q18:

If Aik=6+ and Bijk=2+4+7, find the measure of the angle between the two vectors rounded to the nearest hundredth.

Q19:

Determine the angle between the vectors 211 and 101 in .

  • A a r c c o s 3 2
  • B 3 2
  • C0
  • D 𝜋 2

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