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.

This lesson includes 23 additional questions and 153 additional question variations for subscribers.

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