Vectors Cheat Sheet: A Comprehensive Guide to Vector Operations, Cheat Sheet of Vector Analysis

Vectors Cheat Sheet

Vector Magnitude

‖〈𝑎,𝑏〉‖=√𝑎2+𝑏2

Unit Vector (Normalizing a Vector)

Divide by the magnitude: 𝑢

‖𝑢

‖

〈𝑎,𝑏〉∙〈𝑐,𝑑〉=𝑎𝑐+𝑏𝑑

(𝑎𝚤+𝑏𝚥)×(𝑐𝚤+𝑑𝚥)=𝑎𝑐+𝑏𝑑

Alternative formula: 𝑢

∙𝑣=‖𝑢

〈𝑎,𝑏,𝑐〉×〈𝑑,𝑒,𝑓〉=〈𝑏𝑓−𝑒𝑐, −(𝑎𝑓−𝑑𝑐), 𝑎𝑒−𝑑𝑏〉

Magnitude of the cross product: ‖𝑢

Finding the direction of a single vector: tan 𝜃=𝑦

Finding the angle separating two vectors: cos 𝜃=𝑢

∙𝑣

‖𝑢

‖ ‖𝑣

‖