---
title: "EC.AR.3: 3D Vectors and Analytic Geometry (Georgia Mathematics standard)"
code: EC.AR.3
cite_as: Georgia Standards of Excellence, Mathematics, EC.AR.3
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/EC.AR.3
md_url: https://georgiahomeroom.org/standards/code/EC.AR.3.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/EC.AR.3.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# EC.AR.3: 3D Vectors and Analytic Geometry

Using the engineering design process, express spatial and functional relationships with vectors, functions, and analytic geometry in three dimensions, and use these relationships to solve real-life, contextual, mathematical problems and to explain engineering-based phenomena.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- Express the relationships between points, lines, and planes in three dimensions.
  - **EC.AR.3.1**: Determine the equations of lines and surfaces using vectors and 3D graphing.
  - **EC.AR.3.2**: Apply dot and cross products of vectors to express equations of planes, parallelism, perpendicularity, angles.
  - **EC.AR.3.3**: Describe the role of vectors in engineering applications, such as modeling the velocity of moving objects or static forces on structures and objects.
  - **EC.AR.3.4**: Evaluate matrices and apply their properties to solve problems expressed as matrix equations.
- Investigate functions of two and three independent variables to model engineering systems.
  - **EC.AR.3.5**: Compute limits of scalar and vector-valued functions.
  - **EC.AR.3.6**: Identify and graph level curves of multivariate functions.
  - **EC.AR.3.7**: Find the regions of continuity of multivariate functions.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.