Handout
Other

Rochester Institute of Tech: Cartesian Coordinate System

For Students 9th - 10th Standards
A picture is shown to represent a position vector in three dimensions. The page explains that a position vector may be named at any point along a curve, and the criterion for a position vector.
Unit Plan
OpenStax

Open Stax: Vectors, Scalars, and Coordinate Systems

For Students 9th - 10th
In this interactive module, students will learn how to define and distinguish between scalar and vector quantities. They will assign a coordinate system for a scenario involving one-dimensional motion.
Unit Plan
Wolfram Research

Wolfram Math World: Plane

For Students 9th - 10th
This site defines a plane in terms of geometric surfaces. Content includes formulas for a plane using the normal vector, how to find the x, y, and z intercepts of a plane, distance from the origin, point plane distance formula, dihedral...
Unit Plan
NASA

Nasa: Vectors

For Students 9th - 10th
This site from NASA provides an excellent tutorial on vectors and their use in physics to describe the motion of objects. Vector addition and resolution are illustrated.
Unit Plan
CK-12 Foundation

Ck 12: Analysis: Planes in Space

For Students 11th - 12th
[Free Registration/Login may be required to access all resource tools.] The equation of a plane on an x, y, z coordinate graph
Unit Plan
CK-12 Foundation

Ck 12: Vector Sum and Difference

For Students 9th - 10th Standards
[Free Registration/Login may be required to access all resource tools.] Looks at finding the direction and magnitude of vectors and breaking vectors into component parts.
Unit Plan
CK-12 Foundation

Ck 12: Analysis: Polar and Cartesian Transformation

For Students 11th - 12th
[Free Registration/Login may be required to access all resource tools.] Converting between polar and cartesian coordinates
Graphic
Other

Vector Equation of a Plane

For Students 9th - 10th Standards
This site explains how to find the vector equation of a plane given either the normal vector and a point in the plane or three distinct points in the plane.
eBook
Physics Classroom

The Physics Classroom: Vectors and Projectiles: The Plane and the Wind

For Students 9th - 10th
Observe the three planes in an animation where each plane flies amidst a wind that blows at 20 mph. Learn how tailwinds affect the resultant velocities.
eBook
Physics Classroom

The Physics Classroom: Vectors and Projectiles: The Plane and the Package

For Students 9th - 10th
Consider a plane moving with a constant speed at an elevated height above the Earth's surface. In the course of its flight, the plane drops a package from its luggage compartment. This animation depicts such a situation. The path of the...
Unit Plan
CK-12 Foundation

Ck 12: Analysis: Vector Equation of a Line

For Students 11th - 12th Standards
[Free Registration/Login may be required to access all resource tools.] Finding the Vector equation of a line in three dimensions
Unit Plan
CK-12 Foundation

Ck 12: Analysis: Two Dimensional Vectors

For Students 11th - 12th
[Free Registration/Login may be required to access all resource tools.] Introduction to vector notation in two dimensions
Graphic
University of Nebraska

Rectangular Coordinates in 3 D

For Students 9th - 10th Standards
Advanced discussion of the components of a vector on a three dimensional plane is available here along with formulas and properties.
Website
University of Virginia

Uva Physics: Using Vectors to Describe Motion

For Students 9th - 10th
Background information on vectors and their use in describing motion in two dimensions. A comparison of Aristotle's and Galileo's perspectives on force and motion is given.
Handout
Wolfram Research

Wolfram Math World: Polar Coordinates

For Students 9th - 10th
This math link contains a plethora of information on Polar coordinates. The site begins with a diagram illustrating the measurements used when working with polar coordinates then goes into detail on specifics of using this coordinate...
PPT
Sophia Learning

Sophia: Representing Forces on an Inclined Plane: Lesson 2

For Students 9th - 10th
This lesson demonstrates how to draw free-body diagrams for objects at rest or sliding on an inclined plane. It is 2 of 2 in the series titled "Representing Forces on an Inclined Plane."
Activity
Interactive Mathematics

Interactive Mathematics: Polar Form of Complex Numbers

For Students 9th - 10th Standards
Using vectors as a starting point, this site demonstrates how complex numbers can be written in polar form. Several examples are included that require you to write complex numbers in polar and rectangular form and also represent them...
Unit Plan
CK-12 Foundation

Ck 12: Applications of Matrices

For Students 9th - 10th Standards
[Free Registration/Login may be required to access all resource tools.] Provides resources for working with 2 x 2 matrices as transformations of the plane, and interpreting the absolute value of the determinant in terms of area.
Activity
Paul Dawkins

Paul's Online Notes: Calculus Iii: Applications of Partial Derivatives

For Students 9th - 10th
The resource examines applications of partial derivatives. Topics investigated are tangent planes, linear approximation, gradient vector, and Lagrange multipliers. Class notes, definitions, and examples with detailed solutions are...
Unit Plan
Math Planet

Math Planet: Geometry: Transformation Using Matrices

For Students 9th - 10th Standards
Explains how simple polygons translate into matrices and how to use 2x2 matrices to represent transformations in a plane. Includes video demonstrating an example where a vector must be rotated 90 degrees using matrices. [4:18]
Interactive
Walter Fendt

Walter Fendt: Apps Zur Physik

For Students 9th - 10th
This site, in German, offers numerous apps that illustrate common physics principles. Apps are organized into categories: mechanics, oscillations and waves, electrodynamics, optics, thermodynamics, the theory of relativity, physics of...
Activity
University of Georgia

University of Georgia: Transformations: Revisiting Congruence

For Students 9th - 10th Standards
This site presents information on the three basic transformations of figures in a plane: Reflections, Rotations, and Translations.