Basics
Basics is an interactive experiment in Vectors, a free simulation from StudyFi Lab that runs right in your browser.
A vector has a size and a direction. We write it with coordinates a = (a₁, a₂, a₃) or with the unit vectors of the axes as a = a₁i + a₂j + a₃k. Its length comes from Pythagoras, |a| = √(a₁² + a₂² + a₃²), and the unit vector â = a / |a| keeps the direction with length 1. The vector from point A to point B is the difference B − A.
Try this: Drag the tip to (3, 4) and check that |a| = 5. Then switch on “From two points” and move both points by the same amount: the vector stays the same.
Frequently asked questions
What does the “Basics” experiment show?
A vector has a size and a direction. We write it with coordinates a = (a₁, a₂, a₃) or with the unit vectors of the axes as a = a₁i + a₂j + a₃k. Its length comes from Pythagoras, |a| = √(a₁² + a₂² + a₃²), and the unit vector â = a / |a| keeps the direction with length 1. The vector from point A to point B is the difference B − A.
How do I try “Basics”?
Drag the tip to (3, 4) and check that |a| = 5. Then switch on “From two points” and move both points by the same amount: the vector stays the same.
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