vector quantity
Let an agent explain vector quantities and their mathematics, perform vector calculations, and distinguish vectors from scalars and other quantities in physics and engineering.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Identify Vector or scalar.
Test
Is it a vector.
Test
Classification.
- Does this quantity have a direction, and does it add as a vector? boundary
- Is it a true vector or a pseudovector? definition
Examples
Common vectors.
Examples
Examples.
- Which common quantities are vectors, and what are their scalar counterparts? definition
- How is speed related to velocity? definition
Compute Vector algebra.
Add
Addition and components.
Add
Addition.
- What is the resultant of these vectors, and what are its components? measurement
- How is a vector resolved along axes? action
Products
Dot and cross products.
Products
Products.
- What are the dot and cross products of these vectors, and what do they mean physically? measurement
- When is each used? definition
Fields Vector fields.
Field
Fields.
Field
Fields.
- What is a vector field, and how are electric, magnetic and flow fields represented? definition
- What do divergence and curl describe? definition
Flux
Flux and current density.
Flux
Flux.
- How are mass flow and current density defined as vectors? definition
- How is flux through a surface computed? measurement
Teach Learning vectors.
Intuition
Building intuition.
Intuition
Intuition.
- How can vectors be taught with arrows, motion and forces? action
- Which misconceptions arise? provenance
Notation
Conventions.
Notation
Notation.
- Which notation conventions apply in this field? provenance
- How are vectors written in text and code? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- rotational acceleration, magnetic polarization, particle current density, rotational velocity, dielectric polarization, mass flow, force density, magnetic tension force, angular impulse, displacement current density, total current density, magnetic dipole moment
What it is Filled
A physical quantity that has both magnitude and direction, such as velocity, force, acceleration, electric field, momentum, magnetisation and mass flux density, represented by arrows or component arrays and combined by vector addition; vector quantities contrast with scalar quantities, which have magnitude only.
Why it exists Filled
Let an agent explain vector quantities and their mathematics, perform vector calculations, and distinguish vectors from scalars and other quantities in physics and engineering.
Distinguishing features Filled
- Magnitude and direction
- Vector addition
- Components in a frame
- Transform under rotation
What robots and AI may and may not do Filled
Must not
- Add magnitudes of vectors as if they were scalars in results others rely on.
- Mix reference frames or sign conventions without stating them.
- Present a pseudovector, such as angular momentum, as an ordinary vector where the difference matters.
- Hide uncertainty in calculated loads or forces used for safety decisions.
Only with a human decision
- Using vector results to sign off a design or safety calculation.
May
- Explain vectors and scalars and perform vector calculations with stated frames and units.
- Check that results keep direction, sign convention and reference frame consistent.
Moral aspects Filled
- Errors in force or velocity vectors can make structures, vehicles or flight paths unsafe.
- Teaching material should be accurate so learners are not misled.
Who is affected
- Engineers and students
- People who depend on calculated designs
Owners Filled
Steward
Nobody owns the concept; it is held in common by physics and mathematics.
Links to other meta-models Filled
parent
- Q107715 - registry parent class
related
- physical quantity - category
- magnetization - example
- matrix - component arrays
- speed - a scalar
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.vector-quantity
- Wikidata: Q2672914 (https://www.wikidata.org/wiki/Q2672914)
Direct properties not applicable Not applicable
Not applicable
Plane XCT: no invented physical properties.
Recognition optional Filled
- Magnitude and direction
- Bold or arrow notation
- Scalars such as mass and temperature have no direction
- Not physical; arrows and component notation.
Capabilities and actions required Filled
- identify whether a quantity is a vector
- add, resolve and multiply vectors
- explain vector fields
- apply vectors in mechanics and electromagnetism
Hazards and failure modes required Filled
- Adding magnitudes instead of vectors
- Confusing vectors and pseudovectors
- Frame and sign errors
Standards and interfaces required Filled
- ISO 80000-2 notation for vectors
- SI units
Context of use required Filled
- Describing directional physical quantities.
- kinematic vectors such as velocity and acceleration
- dynamic vectors such as force and momentum
- field vectors such as electric and magnetic fields
- flux and current density vectors
- pseudovectors such as angular velocity
Sources Filled
- Wikidata item Q2672914: vector quantity - identity and sense of the item
- Wikipedia: Vector quantity - general description of the item
Open questions
- Should vector fields be a separate entry?
- How should notation conventions be linked?
- How should teaching resources be linked?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q2672914/spec.json