Practice Flashcards
What is a vector?
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All Flashcards in Topic 3.12
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3.12.18 cards
What is a vector?
A quantity with both direction and magnitude (size). It's a 'how far across / up / out' instruction with no fixed starting point.
What do i, j, k stand for?
Unit steps along the x, y and z axes: i = (1,0,0)ᵀ, j = (0,1,0)ᵀ, k = (0,0,1)ᵀ.
Write 4i − j + 2k in column form.
(4, −1, 2)ᵀ — the coefficients of i, j, k stacked.
Formula for the magnitude of a vector?
|v| = √(x² + y² + z²): square each component, add, take the positive square root.
Magnitude of (3, 4)ᵀ?
√(3² + 4²) = √25 = 5.
Magnitude of (2, −3, 6)ᵀ?
√(4 + 9 + 36) = √49 = 7.
Can a magnitude be negative?
No — it's a length, so |v| ≥ 0 always.
(k, 12)ᵀ has magnitude 13. Find k.
k² + 144 = 169 ⇒ k² = 25 ⇒ k = ±5.
3.12.28 cards
What is a unit vector?
A vector with magnitude (length) exactly 1, used to specify a direction.
How do you find the unit vector in the direction of v?
Divide v by its magnitude: v̂ = v / |v|.
Unit vector in the direction of (3, 4)ᵀ?
|v| = 5, so v̂ = (3/5, 4/5)ᵀ = 0.6i + 0.8j.
What is the position vector of a point A?
The vector OA from the origin to A — its components are A's coordinates.
Formula for the vector from A to B?
AB = OB − OA (finish minus start).
How do you find the distance between points A and B?
Compute AB = OB − OA, then take its magnitude |AB|.
OA = (1, 2)ᵀ, OB = (4, 6)ᵀ. Find AB and |AB|.
AB = (3, 4)ᵀ, |AB| = √25 = 5.
How do you make a vector of length k in the direction of v?
Find the unit vector v/|v|, then multiply it by k.
Topic 3.12 study notes
Full notes & explanations for Vectors (HL only)
Math AA exam skills
Paper structures, command terms & tips
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