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Subject:  Linear Algebra

Angle between (1, 0) and (1, 1)

Use the dot product to find the angle between two 2D vectors.

Answer a · b = 1, |a| = 1, |b| = 1.41421, angle = 45°

Solution

  1. Vectors a = (1, 0), b = (1, 1)
  2. Magnitudes |a| = 1, |b| = 1.41421
  3. Dot product a · b = 1
  4. Cross product (2D scalar) a × b = 1
  5. Angle between θ = arccos(a·b / (|a||b|)) = 45°

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