Vector Algebra: One-Page Formula Sheet

Vector Algebra — formula sheet

Formulas

• a·b = |a||b| cosθ
• |a × b| = |a||b| sinθ
• Projection of a on b = a·b/|b|
• a × (b × c) = (a·c)b − (a·b)c

Key ideas

• Dot product measures projection; zero for perpendicular vectors
• Cross product is perpendicular to both; magnitude = area of parallelogram
• Scalar triple product = volume of parallelepiped
• Coplanar vectors: [a b c] = 0

Traps to avoid

• Cross product order (a × b = −b × a)
• Using dot product for area
• Wrong expansion of vector triple product

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