Lesson Worksheet: Angle between Two Vectors in Space Mathematics • 12th Grade

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

Q1:

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

Q2:

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

Q3:

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

Q4:

Given that ||=35A, ||=23B, and AB⋅=−805√22, determine the measure of the smaller angle between the two vectors.

Q5:

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

Q6:

Find the angle between the vector A=⟨9,10,−4⟩ and the unit vector j. Round your answer to the nearest degree.

Q7:

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.

Q8:

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

Q9:

If A and B are two perpendicular unit vectors, find (3−)⋅(−2+)ABAB.

Q10:

Find the measure of the angle between the two vectors shown in the figure. Round your answer to the nearest degree.

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