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All 8 Flashcards — Vectors as components & magnitude
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Question
What is a vector?
Answer
A quantity with both direction and magnitude (size). It's a 'how far across / up / out' instruction with no fixed starting point.
Question
What do i, j, k stand for?
Answer
Unit steps along the x, y and z axes: i = (1,0,0)ᵀ, j = (0,1,0)ᵀ, k = (0,0,1)ᵀ.
Question
Write 4i − j + 2k in column form.
Answer
(4, −1, 2)ᵀ — the coefficients of i, j, k stacked.
Question
Formula for the magnitude of a vector?
Answer
|v| = √(x² + y² + z²): square each component, add, take the positive square root.
Question
Magnitude of (3, 4)ᵀ?
Answer
√(3² + 4²) = √25 = 5.
Question
Magnitude of (2, −3, 6)ᵀ?
Answer
√(4 + 9 + 36) = √49 = 7.
Question
Can a magnitude be negative?
Answer
No — it's a length, so |v| ≥ 0 always.
Question
(k, 12)ᵀ has magnitude 13. Find k.
Answer
k² + 144 = 169 ⇒ k² = 25 ⇒ k = ±5.
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Full study notes for Vectors as components & magnitude
Topic 3.12 hub
Vectors (HL only)
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