Porisma
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Vectors: magnitude, direction and products

Work with Cartesian vectors · Diagrams · Complete reading

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Position, displacement and translation in two dimensions

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Equal-scale xy grids. Left: A(4,3),B(2,4), position arrows OA, OB and displacement A→B, with unit i,j. Right: P(1,4) maps to Q(4,3) by v=(3,−1); OP+v=OQ.
Equal-scale xy grids. Left: A(4,3),B(2,4), position arrows OA, OB and displacement A→B, with unit i,j. Right: P(1,4) maps to Q(4,3) by v=(3,−1); OP+v=OQ.
Equal-scale xy grids. Left: A(4,3),B(2,4), position arrows OA, OB and displacement A→B, with unit i,j. Right: P(1,4) maps to Q(4,3) by v=(3,−1); OP+v=OQ.
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Three-dimensional coordinate decomposition

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Schematic source projection: A(x,0,0),B(0,y,0),C(0,0,z),R(x,y,0),P(x,y,z), mutually perpendicular coordinate axes and basis i,j,k. Dashed projections and right-angle markers show OR in the xy-plane and RP parallel to z; OP is the resultant.
Schematic source projection: A(x,0,0),B(0,y,0),C(0,0,z),R(x,y,0),P(x,y,z), mutually perpendicular coordinate axes and basis i,j,k. Dashed projections and right-angle markers show OR in the xy-plane and RP parallel to z; OP is the resultant.
Schematic source projection: A(x,0,0),B(0,y,0),C(0,0,z),R(x,y,0),P(x,y,z), mutually perpendicular coordinate axes and basis i,j,k. Dashed projections and right-angle markers show OR in the xy-plane and RP parallel to z; OP is the resultant.
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Right-handed coordinate directions

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Curl the right-hand fingers from positive x to positive y; the thumb gives positive z. The source hand’s direction role is represented by the labelled turn and +z arrow. Spatial orthogonality does not imply right angles in this projected picture.
Curl the right-hand fingers from positive x to positive y; the thumb gives positive z. The source hand’s direction role is represented by the labelled turn and +z arrow. Spatial orthogonality does not imply right angles in this projected picture.
Curl the right-hand fingers from positive x to positive y; the thumb gives positive z. The source hand’s direction role is represented by the labelled turn and +z arrow. Spatial orthogonality does not imply right angles in this projected picture.
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