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Subject:  Linear Algebra

Magnitude of the vector (3, 4)

The Pythagorean theorem gives the length of a 2D vector.

Answer a · b = 3, |a| = 5, |b| = 1, angle = 53.1301°

Solution

  1. Vectors a = (3, 4), b = (1, 0)
  2. Magnitudes |a| = 5, |b| = 1
  3. Dot product a · b = 3
  4. Cross product (2D scalar) a × b = -4
  5. Angle between θ = arccos(a·b / (|a||b|)) = 53.1301°

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