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Flip to reveal answersWhat is a unit vector?
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All 8 Flashcards — Unit & position vectors
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Question
What is a unit vector?
Answer
A vector with magnitude (length) exactly 1, used to specify a direction.
Question
How do you find the unit vector in the direction of v?
Answer
Divide v by its magnitude: v̂ = v / |v|.
Question
Unit vector in the direction of (3, 4)ᵀ?
Answer
|v| = 5, so v̂ = (3/5, 4/5)ᵀ = 0.6i + 0.8j.
Question
What is the position vector of a point A?
Answer
The vector OA from the origin to A — its components are A's coordinates.
Question
Formula for the vector from A to B?
Answer
AB = OB − OA (finish minus start).
Question
How do you find the distance between points A and B?
Answer
Compute AB = OB − OA, then take its magnitude |AB|.
Question
OA = (1, 2)ᵀ, OB = (4, 6)ᵀ. Find AB and |AB|.
Answer
AB = (3, 4)ᵀ, |AB| = √25 = 5.
Question
How do you make a vector of length k in the direction of v?
Answer
Find the unit vector v/|v|, then multiply it by k.
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Full study notes for Unit & position vectors
Topic 3.12 hub
Vectors (HL only)
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