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