Practice Flashcards
What two pieces of information does a vector store?
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All Flashcards in Topic 3.10
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3.10.18 cards
What two pieces of information does a vector store?
A magnitude (size) and a direction. A scalar has size only (e.g. temperature, price).
How do you find the magnitude of a vector?
Pythagoras on its components: |v| = √(v₁² + v₂²) in 2D, √(v₁² + v₂² + v₃²) in 3D.
Magnitude of (6, 8)?
√(6² + 8²) = √100 = 10.
How do you add or subtract two vectors?
Component by component: add (or subtract) the matching entries.
What does scalar multiplication k·v do to a vector?
Multiplies every component by k — it stretches/shrinks the vector, and flips its direction if k is negative.
How do you make a unit vector from v?
Divide v by its own magnitude: v̂ = v / |v|. It keeps the direction but has length 1.
What is a position vector?
The arrow from the origin O to a point: the position vector of A is a = OA.
What is AB in terms of the position vectors a and b?
AB = b − a ('finish minus start') — the displacement from A to B.
Topic 3.10 study notes
Full notes & explanations for Vector definitions (HL only)
Math AI exam skills
Paper structures, command terms & tips
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