Mathematics — first biennium · Lesson
The dot product connects components and geometry: u·v=uₓvₓ+uᵧvᵧ. Its sign distinguishes acute, right and obtuse angles; in particular u·v=0 for non-zero perpendicular vectors.
Prerequisites: Dependence, components and plane geometry
Goal: Calculate the dot product and interpret its sign with respect to the angle between two vectors.
In this lesson: Calculate the dot product and interpret its sign with respect to the angle between two vectors.
New concept: The dot product u·v=uxvx+uyvy produces a number, not a vector. Its sign describes the angle: positive for an acute angle, zero for perpendicular vectors, and negative for an obtuse angle.
How to proceed: After calculating, use the sign: positive → acute, zero → right, negative → obtuse/straight.
You can already assume: Dependence, components and plane geometry.
The diagram lets you compare the sign of the dot product with the visible angle between the two arrows.
Completed exercises: 0/5 · Correct on first attempt: 0
After calculating, use the sign: positive → acute, zero → right, negative → obtuse/straight.
Data / situation: u=(2,-1), v=(2,-1).
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.