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Year 12 · Shapes & Geometry

Magnitude and dot product

A vector has size and direction, written (x, y). Add component by component; the magnitude comes from Pythagoras.

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How to do it

  1. Add or subtract matching components.
  2. Scalar: multiply both components.
  3. Magnitude √(x² + y²). Dot product x₁x₂ + y₁y₂.

Worked example

Find the magnitude of the vector (5, 12).
|v| = √(x² + y²) = √(5² + 12²) = √169 = 13.
Answer: 13

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The dot product is a number, not a vector.

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