This lesson is perfect for a precalculus or geometry class studying vectors. Students can work in partners or groups to complete the in-class lesson, which gives students the definitions of dot product and orthogonality, as well as a formula for how to find the angle between vectors, and then asks them to think critically and apply the knowledge to problems. They prove properties about the dot product, think through how to use the formula for the angle between to vectors to find another way to compute the dot product, and think about how the definition of orthogonality (dot product is equal to zero) tells us about the angle between orthogonal vectors. The homework isn't just simply practice problems--it demands critical thinking to apply the knowledge gained from the in-class notes to problems they have not yet seen before. The homework encourages critical thinking, problem-solving, and applying knowledge to new problems.
Check out my other vector lessons:
Introduction to Vectors Guided Notes and Homework
Vector Operations Guided Notes and Homework
Vectors Task Cards Activity
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