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Concept · Geometry & Algebra
Dot product
definition, coordinate form, magnitude of a sum via law of cosines, angle between vectors, perpendicularity, projection vector
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Key formulas
6- Coordinates of ABB − A (component-wise)magnitude |a| = √ax2 + ay2 (+ az2)
- Dot producta·b = |a||b| cos θ = ax bx + ay by (+ az bz)
- Angle between vectorscos θ = (a·b)/(|a||b|)
- Perpendicular: a·b = 0Parallel/collinear (2D): ax by − ay bx = 0 (components proportional)
- Magnitude of a sum|a+b|2 = |a|2 + 2(a·b) + |b|2
- Projection vector of a onto b((a·b)/|b|2) bscalar projection (a·b)/|b|
Shaky underneath?
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FoundationsPrecalculus bridgeAlgebra 2 foundations