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Key Concepts
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1. Definition
The cross product (vector product) results in a vector perpendicular to both vectors.
a × b = (|a| |b| sin θ) n̂
2. Properties
- a × b = -(b × a) (Anti-commutative)
- If a × b = 0, the vectors are parallel.
- i × j = k, j × k = i, k × i = j
3. Geometrical Application
- Area of Parallelogram: |a × b|, where a and b are adjacent sides.
- Area of Triangle: ½|a × b|.