How we worked it out
Updated as you change the numbers.
- a · b = Σ aᵢbᵢ. a × b = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁). Angle = arccos(a · b ÷ (|a||b|)).
Method and assumptions
2D vectors are treated as 3D with z = 0, so their cross product points along z.
Questions
What is the dot product of (3, −2, 5) and (1, 4, −2)?
−15; the vectors are about 122.1° apart.
Sources
Method and figures checked on . Every worked answer on this page is covered by an automated test. Found a mistake? Tell us.