Lesson: Geometric Applications of Vectors Mathematics

In this lesson, we will learn how to use vector operations and vector properties to solve problems involving geometrical shapes.

Lesson Plan

Objectives

Students will be able to

  • use vector operations and vector properties to solve problems involving geometric shapes,
  • use vector operations and vector properties to prove geometric theorems and relations.

Prerequisites

Students should already be familiar with

  • vectors and vector notation,
  • triangle vector formula,
  • vector addition and subtraction,
  • vector magnitude.

Exclusions

Students will not cover

  • problems requiring the scalar or vector products,
  • real-life problems including speed or forces.

Lesson Video

Video Thumbnail
15:22

Lesson Explainer

Sample Question Videos

  • 05:31
  • 03:36
  • 02:32

Lesson Worksheet

Q1:

𝐴𝐡𝐢𝐷 is a square, in which the coordinates of the points 𝐴, 𝐡, and 𝐢 are (1,βˆ’8), (3,βˆ’10), and (5,βˆ’8). Use vectors to determine the coordinates of the point 𝐷 and the area of the square.

Q2:

Trapezoid 𝐴𝐡𝐢𝐷 has vertices 𝐴(4,14), 𝐡(4,βˆ’4), 𝐢(βˆ’12,βˆ’4), and 𝐷(βˆ’12,9). Given that 𝐴𝐡βˆ₯𝐷𝐢 and οƒ π΄π΅βŸ‚οƒŸπΆπ΅, find the area of that trapezoid.

Q3:

Given a trapezoid 𝐴𝐡𝐢𝐷, in which 𝐴𝐷βˆ₯𝐡𝐢 and 𝐴𝐷𝐡𝐢=7, find the value of π‘˜ such that 𝐴𝐢+𝐡𝐷=π‘˜οƒ π΄π·.

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