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.
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
Related posters
Charts that sit alongside Dot & Cross Product on the same wall.
Browse every Mathematics poster, or start from the full catalogue.