Dot & Cross ProductTwo products: different outputs, different geometry, different laws.MathematicsDot productOutput is a scalaru · v = |u||v| cos θZero exactly when perpendicularCommutative: u · v = v · uDefined in every ℝⁿGives lengths, angles andprojectionsCross productOutput is a vector|u × v| = |u||v| sin θZero exactly when parallelAnticommutative: u × v = −(v × u)Defined only in ℝ³Gives areas, normals andmomentsTHE DIFFERENCE THAT MATTERSThe dot product measures how far two vectors agree; the crossproduct measures how far they do not.For nonzero vectors, u · v = 0 and u × v = 0 cannot both hold:perpendicular and parallel are exclusive.Dot & Cross Productlearnposters.com
Dot & Cross Product — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Dot & Cross Product poster

Dot product against Cross product, side by side.

For nonzero vectors, u · v = 0 and u × v = 0 cannot both hold: perpendicular and parallel are exclusive.

Questions about the Dot & Cross Product poster

What’s on the Dot & Cross Product poster?
Dot product against Cross product, side by side. Dot product: Output is a scalar; Dot product: u · v = |u||v| cos θ; Dot product: Zero exactly when perpendicular; Dot product: Commutative: u · v = v · u; Dot product: Defined in every ℝⁿ; Dot product: Gives lengths, angles and projections; Cross product: Output is a vector; Cross product: |u × v| = |u||v| sin θ; Cross product: Zero exactly when parallel; Cross product: Anticommutative: u × v = −(v × u); Cross product: Defined only in ℝ³; Cross product: Gives areas, normals and moments; The dot product measures how far two vectors agree; the cross product measures how fa…. For nonzero vectors, u · v = 0 and u × v = 0 cannot both hold: perpendicular and parallel are exclusive.
Who is the Dot & Cross Product poster for?
Dot & Cross Product belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning linear algebra can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Dot & Cross Product poster?
Dot for angles and projections; cross for normals, areas and moments. A wall chart earns its place by being glanceable from where the work is happening, so Dot & Cross Product belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Dot & Cross Product?
Basis & Dimension, Determinant Properties and Diagonalisation sit alongside Dot & Cross Product in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Basis & DimensionDeterminant PropertiesDiagonalisation
Is the Dot & Cross Product poster free to download and print?
Yes. Dot & Cross Product downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Dot & Cross Product poster print at?
Dot & Cross Product is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Dot & Cross Product loses nothing.Printing guide

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