PEAZIT Aha card
Go straight to resources ↓The dot product compares directions
In perpendicular coordinates, multiply matching components and add. For nonzero vectors, a zero result means perpendicular directions.
| Relation | Meaning |
|---|---|
| u · v = u₁v₁ + u₂v₂ | Pair first components together and second components together. |
| u = (2; 1); v = (3; −2) | Keep the negative component's sign. |
| u · v = 2 × 3 + 1 × (−2) = 4 | The result is a number, not a vector. |
One worked example
- u · v = u₁v₁ + u₂v₂Pair first components together and second components together.
- u = (2; 1); v = (3; −2)Keep the negative component's sign.
- u · v = 2 × 3 + 1 × (−2) = 4The result is a number, not a vector.
Watch out: The zero vector has zero dot product with every vector but no defined direction. Angle interpretation requires nonzero vectors.
Goal, prerequisites and card origin
What you will learn: Calculate a dot product and recognize perpendicular nonzero vectors.
What you need first: Vector components and signed multiplication.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
In perpendicular coordinates, multiply matching components and add. For nonzero vectors, a zero result means perpendicular directions.