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Subject:  Linear Algebra

Dot product (1, 2, 3) · (4, 5, 6)

Multiply matching components and sum to find the dot product.

Answer a × b = (-3, 6, -3), a · b = 32, |a| = 3.74166, |b| = 8.77496, angle = 12.9332°

Solution

  1. Vectors a = (1, 2, 3), b = (4, 5, 6)
  2. Magnitudes |a| = 3.74166, |b| = 8.77496
  3. Dot product a · b = 32
  4. Cross product a × b = (-3, 6, -3)
  5. Angle between θ = arccos(a·b / (|a||b|)) = 12.9332°

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