The Dot Product

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Vectors pop up in a ton of science and linear algebra applications, so becoming familiar with their basic manipulations and arithmetic is a must for pupils with an eye on higher math and science. Enter this skill-based lesson on finding the dot product of vector pairs. Clear and concise in explanation, with many built in examples, this resource is a great introduction to the concept of dot products. Particularly effective if the class has not yet studied matrix multiplication, this lesson does not rely on a familiarity with matrix properties as many covering this topic do.

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CCSS: Adaptable
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Instructional Ideas
  • Have each learner draw and label a vector, and then partner with classmates to find the dot product of their respective vectors
  • Consider leading an investigation into what kind of vectors are orthogonal, and what characteristics (slope, direction, magnitude) influence this property
  • Give the class a scalar number, with the assignment to create a vector pair with the given dot product result
Classroom Considerations
  • Class notes to match the main resource presentation are available under additional resources
  • Presentation would make for a fabuolous interactive whiteboard lesson, with each step or problem revealed as solved by the class
  • This resource is only available on an unencrypted HTTP website. It should be fine for general use, but don’t use it to share any personally identifiable information
  • Each section is introduced with a summary of key concepts and strategies
  • Example problems build in complexity as the lesson progresses
  • Orthogonal vectors covered thoroughly and in a variety of appearances 
  • No explanation or graphics for what it physically means for two vectors to be orthogonal