Home › Adventure Map › Advanced_geometry › Vectors
← Return to Adventure Map

Vectors

The Hook

Despicable Me's Vector.

What is it?

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

Time Travel (History)

Developed to calculate complex forces in bridges and electricity.

Cheat Code

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

Practice This Now!

The Field Guide

In 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).

In The Real World: 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.
⚠

Booby Trap!

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

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

Training Drills

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