Curated OER
MA 371 - Vector Norm: Dot Product
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...
Curated OER
Applications of the Cross Product and Dot Product
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...
Curated OER
Worksheet 8 - Vectors
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...
Curated OER
Math 212: Dot Product and Cross Product
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.
Curated OER
Multivariable Calculus: Dot Product
In this dot product learning exercise, students identify the properties of the dot product. They sketch vectors and obtain expressions for diagonals. This two-page learning exercise contains examples and explanations with two problems.
Curated OER
Math 224 Spring 2004: Dot Product
For 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.
Curated OER
Linear Systems: Lengths and Dot Products
In this dot product activity, students explore the multiplication of vectors. This two-page activity contains explanations, examples, and approximately ten problems.
Curated OER
Worksheet 4 - Geometric Mean
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...
EngageNY
Expected Value of a Discrete Random Variable
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.
Curated OER
Worksheet 22 - Functions
For 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.
Curated OER
Linear Systems
For this multiplication of vectors worksheet, students 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...
Curated OER
Alignment of a Solar Panel: Dot and Cross Products
In this dot and cross product learning exercise, students identify vector points under given conditions determine vertical support and determine angles of an object. This two-page learning exercise contains two problems.
Curated OER
Lengths and Dot Sequences
In this math learning exercise, students examine the process of multiplying vectors to find their products. They practice finding the geometric and algebraic views for the solutions.
Curated OER
Worksheet 20
In this math worksheet, students investigate the given vectors. Then they apply the knowledge to prove the formula for the triangle formed by them.
Curated OER
Worksheet 21
In this math instructional activity, learners draw two vectors u and v based at the same point. The vectors are considered neither parallel nor orthogonal.
Curated OER
Worksheet 31
In this math worksheet, students investigate vectors and polar coordinates. They convert the paths of polar coordinates to Euclidian points.
Curated OER
Linear Systems: Orthogonal Matrices
In this orthogonal matrices learning exercise, students explore characteristics of an orthogonal matrix. They use Gram-Schmidt to convert linearly independent vectors to orthonormal vectors. This three-page learning exercise contains...
Curated OER
MT-A315 Introduction to Linear Algebra
In this algebra worksheet, learners figure out the equation of the general vector, they find the orthogonal basis and apply the formula to solve the problems.
Curated OER
Energy, Work and Power
In this energy, work and power activity, students solve 12 problems about circuits, electric motors, Ohm's Law and electric currents.
Wolfram Research
Wolfram Math World: Dot Product
This math site gives the formula for taking the dot product of two vectors, gives properties of dot products, (commutative, associative, and distributive), how to find the derivative of a dot product. This site has links to several other...
National Council of Teachers of Mathematics
The Math Forum: Dot Product of Unit Vectors
This site gives an example of a problem showing how to find the dot product of unit vectors.
Analyze Math
Analyze Math: Dot Product of Two Vectors and Applications
Learners explore the Pre-Calculus topic of vectors. The activity is a tutorial on the calculation and applications of the dot product of two vectors. Examples with detailed solutions are included.
CK-12 Foundation
Ck 12: Analysis: Dot Products
[Free Registration/Login may be required to access all resource tools.] In this lesson students are calculating dot products of vector quantities. Students examine guided notes, review guided practice, watch instructional videos and...
Paul Dawkins
Paul's Online Notes: Calculus Ii: Vectors
The resource examines vectors and their properties. Topics investigated are vector, vector arithmetic, dot product, and cross product. Class notes, definitions, and examples with detailed solutions are included. The notes are available...