lightbulb Key Concepts

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1. Scalar Projection

The scalar projection of vector a onto vector b is the length of the 'shadow' cast by a on b.

Proj_b a = (a · b) / |b|

2. Vector Projection

The vector projection is the scalar projection multiplied by the unit vector of b:

Proj_v_b a = [(a · b) / |b|²] · b