Instructional Video2:20
Curated OER

#### Finding the Dot Product

For Teachers 9th - 11th
Are you just starting a unit of vectors or matrices? Help your class learn how to find the dot product with this simplistic video tutorial. The procedure is shown as the tutor determines the dot product of A and B by transposing numbers...
Instructional Video14:12
1
1
3Blue1Brown

#### Dot Products and Duality | Essence of Linear Algebra, Chapter 7

For Students 11th - Higher Ed Standards
The dot product of two matrices is a number on the number line, its transformation. The resource presents the dot product as a linear transformation from two dimensions to one dimension. The video uses the numerical and graphical...
Lesson Plan
Curated OER

#### MA 371 - Vector Norm: Dot Product

For Teachers 12th - Higher Ed
In this dot product worksheet, students solve 6 short answer problems. Students find unit vectors in the same direction as a given vector. Students express vectors as a linear combination of the standard basis vectors. Students find a...
Worksheet
Curated OER

#### Applications of the Cross Product and Dot Product

For Students 9th - 12th
In this cross product and dot product worksheet, students solve 2 problems including finding the magnetic field between 2 poles of a magnet and determining angles between vectors in a word problem about television watching given a scale...
Worksheet
Curated OER

#### Math 212: Dot Product and Cross Product

For Students Higher Ed
In this dot product worksheet, students consider vectors, find the value of an angle, and confirm the area of a given parallelogram. This two-page worksheet contains three problems.
Worksheet
Curated OER

#### Math 224 Spring 2004: Dot Product

For Students Higher Ed
In this dot product worksheet, students consider two vectors and compute the dot product and cross product of the given vectors. This two-page worksheet contains four problems.
Worksheet
Curated OER

#### Multivariable Calculus: Dot Product

For Students Higher Ed
In this dot product activity, students identify the properties of the dot product. They sketch vectors and obtain expressions for diagonals. This two-page activity contains examples and explanations with two problems.
Worksheet
Curated OER

#### Linear Systems: Lengths and Dot Products

For Students Higher Ed
In this dot product learning exercise, students explore the multiplication of vectors. This two-page learning exercise contains explanations, examples, and approximately ten problems.
Lesson Plan
Curated OER

#### Worksheet 8 - Vectors

For Teachers Higher Ed
In this vector worksheet, students find the area of a parallelogram spanned by vectors, they give the geometric and algebraic definitions of the dot product and describe a sequence of vectors. This one-page worksheet contains six...
Lesson Plan
EngageNY

#### Expected Value of a Discrete Random Variable

For Teachers 11th - 12th Standards
Discover how to calculate the expected value of a random variable. In the seventh installment of a 21-part module, young mathematicians develop the formula for expected value. They connect this concept the dot product of vectors.
Worksheet
Curated OER

#### Linear Systems

For Students 11th - Higher Ed
In this multiplication of vectors worksheet, learners prove that the dot product operation is commutative. They normalize a vector so it has the same direction with a magnitude of one. Students use the angle formula to confirm...
Lesson Plan
Curated OER

#### Worksheet 4 - Geometric Mean

For Teachers Higher Ed
In this geometric worksheet, students examine the geometric and algebraic definition of the dot product. They find angles between two curves, determine if two vectors are parallel, and explain conditions on vectors. This one-page...
Lesson Plan
Curated OER

#### Vector Addition and Dot Products

For Teachers 12th
Twelfth graders plot vectors on the coordinates and evaluate them. In this physics lesson, 12th graders watch a video tutorial and complete assigned worksheet.
Worksheet
Curated OER

#### Linear Systems: Matrix Operations

For Students Higher Ed
In this matrix operations worksheet, students find the dot product of matrices. They use the elimination method to solve linear equations. This two-page worksheet contains explanations, examples and three problems.
Handout
1
1
Curated OER

#### Math Handbook: Trigonometry

For Students 9th - 12th Standards
You'll be spinning in unit circles once you read through this jumbo-sized resource of everything you need to know about trigonometry. Each page has color-coded examples with explicit directions that detail the problems and formulas.
Instructional Video9:59
1
1
3Blue1Brown

#### Linear Combinations, Span, and Basis Vectors | Essence of Linear Algebra, Chapter 2

For Students 11th - Higher Ed Standards
What does it mean for two vectors to be linearly independent? The resource presents the basics of basis vectors and linear combinations. The third video in the 15-part series provides a definition of linear independence in terms of the...
Worksheet
Curated OER

#### On the Dots

For Students 8th - 10th
If you want your class to practice reading informational texts and answering related questions, this short exercise from The New York Times' "Learning Network" might be helpful. It includes an article on Dippin' Dots and uses...
PPT
Bowels Physics

#### Work, Energy, and Power

For Teachers 9th - 12th Standards
Work, energy, and their relationship to power: what is the common thread? Explore this with your class as they learn the concepts of work and energy, both kinetic and potential, before completing multiple practice problems to demonstrate...
Instructional Video10:04
1
1
3Blue1Brown

#### Matrix Multiplication as Composition | Essence of Linear Algebra, Chapter 4

For Students 11th - Higher Ed Standards
Take a different view at matrix multiplication. Based on vector transformations, the video presents matrix multiplication as the result of the composition of multiple linear transformations. The presentation explains the numerical...
Instructional Video12:09
1
1
3Blue1Brown

#### Inverse Matrices, Column Space and Null Space | Essence of Linear Algebra, Chapter 6

For Students 11th - Higher Ed Standards
Determine the geometric representation to the solution of a system of linear equations. The resource shows how scholars can represent a system of linear equations as a linear transformation. The video discusses using an inverse matrix to...
Instructional Video10:03
1
1
3Blue1Brown

#### The Determinant | Essence of Linear Algebra, Chapter 5

For Students 11th - Higher Ed Standards
Determine how much a linear transformation alters area. The seventh segment in a series of 15 makes the connection between the determinant and the scale factor of areas during a linear transformation. The video goes on to explain the...
Instructional Video10:59
1
1
3Blue1Brown

#### Linear Transformations and Matrices | Essence of Linear Algebra, Chapter 3

For Students 11th - Higher Ed Standards
Are all transformations of the plane linear transformations? The video provides examples of transformations of the plane and provides the definition of linear transformations. The resource begins the discussion of using matrix...
Lesson Plan
Curated OER

#### Worksheet 22 - Functions

For Teachers Higher Ed
In this function worksheet, students use functions to identify an electron traveling along a path. They examine the velocity vector and compute the directional derivative. This two-page worksheet contains six multi-step problems.
Interactive
Curated OER

#### Energy, Work and Power

For Students 10th - 12th
For this energy, work and power worksheet, students solve 12 problems about circuits, electric motors, Ohm's Law and electric currents.