Vector algebra: Some exciting applications

Methane CH4

What is this session about

Vector algebra made interesting

Concepts from vector algebra are introduced at the higher secondary level. If we show students how it helps answer some interesting questions from diverse fields, they will find it more interesting.

Elegant solutions

Vector algebra can lead us to short and elegant proofs/​solutions, when used in conjunction with ideas like symmetry

What do we discuss in this session?

Here we look the applications of vector algebra to answer some questions from trigonometry, geometry, chemistry and astronomy.

  1. Applying vector algebra to derive some trigonometric results in a simple manner
  2. An everyday example of finding the angle between pipes on perpendicular faces of a building
  3. The structure of a molecule like methane, using symmetry arguments
  4. Addressing misconceptions about phases of the Moon using a more involved application of vector algebra

00:00 Introduction
05:21 Dot product to prove trigonometric angle addition formula
09:45 Cosine rule
15:45 Angle between two pipes along two faces of a building
18:07 Is the angle between planes same as the angle between lines in those planes?
27:15 Angles in a tetrahedral Methane molecule
41:00 Explaining phases of the Moon with vector algebra