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Vectors

Overview

Despicable Me's Vector.

What is it?

A quantity that has both Magnitude (size) and Direction.

History

Developed to calculate complex forces in bridges and electricity.

Key Idea

Head to Tail method for adding. Tail is start, Head is the arrow.

Practice This Topic

Concept Guide

Plain English: A number just tells you 'how much' (Scalar). A vector tells you 'how much' AND 'which way'. Speed is a scalar (50mph). Velocity is a vector (50mph North).

Real-world example: Pilots. A plane flies forward at 500mph, but the wind blows sideways at 50mph. The pilot uses vectors to calculate the actual path.

How to do it

  1. Break diagonal vectors into X (horizontal) and Y (vertical) components.
  2. Add all X components together.
  3. Add all Y components together.
  4. Use Pythagoras on the total X and Y to find the final Magnitude.
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Common Pitfall

Adding magnitudes directly. If you walk 3m East and 4m North, you didn't walk 7m total displacement. You walked 5m (hypotenuse).

Word Problem
"You push a box with vector <3, 2>. Your friend helps with vector <1, 5>. What is the total force vector?"
Reasoning: Add the components directly. X: 3+1=4. Y: 2+5=7. Result vector: <4, 7>.

Practice Examples

Component Form
v =
Pointy brackets indicate a vector, not a point.