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Lesson Plan: Direction of 3D Vectors

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find unit vectors in the direction of a given 3D vector and how to calculate the angles formed by 3D vectors.

Objectives

Students will be able to

  • find a unit vector in the same direction of a given 3D vector,
  • find the angle between a 3D vector and a coordinate axis,
  • find angles between 3D vectors using a right triangle,
  • find angles between 3D vectors using the law of cosine,
  • find the angle between a 3D vector and a coordinate plane.

Prerequisites

Students should already be familiar with

  • 3D vectors as column vectors or in terms of ijk,
  • magnitude of a 3D vector,
  • vector addition, subtraction, and scalar multiplication,
  • right triangle trigonometry,
  • the law of cosine,
  • inverse trigonometric functions.

Exclusions

Students will not cover

  • dot products,
  • cross products.

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