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

In this lesson, we will learn how to find the angle between two vectors in space using their dot product.

Lesson Plan

Students will be able to

find the angle between two vectors by finding their dot product and recognize which angle has been calculated,
find the angle between two vectors given graphically by finding their dot product,
find the angle between two vectors by applying properties of vectors before finding their dot product.

Q1:

If and , find the measure of the angle between the two vectors rounded to the nearest hundredth.

Q2:

Find the angle between the vectors and . Give your answer correct to one decimal place.

Q3:

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