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Instructional Video8:54
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\n\"Cross\n\n
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\n3Blue1Brown\n
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\nCross Products | Essence of Linear Algebra, Chapter 8\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nEquate the area of a parallelogram with the magnitude. The 11th installment in a 15-video series introduces the concept of the cross product of two vectors. The presentation makes the geometric connection between the cross product, the...\n
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Lesson Plan
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\n\"Gyroscopes\n\n
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\nCurated OER\n
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\nGyroscopes in Motion\n

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\n\nFor Teachers\n\n10th - 12th\n
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\nPhysics stars will enjoy learning about the conservation of energy as you demonstrate gyroscope precession. The lecture is broken into five subtopics: cross product, rotating vectors, angular momentum, rotating rigid bodies, and torque...\n
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Worksheet
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\n\"Applications\n\n
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\nCurated OER\n
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\nApplications of the Cross Product and Dot Product\n

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\n\nFor Students\n\n9th - 12th\n
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\nIn 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...\n
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Instructional Video9:59
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\n\"Linear\n\n
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\n3Blue1Brown\n
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\nLinear Combinations, Span, and Basis Vectors | Essence of Linear Algebra, Chapter 2\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nWhat 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...\n
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Worksheet
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\n\"Math\n\n
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\nCurated OER\n
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\nMath 212: Dot Product and Cross Product\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn 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.\n
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Worksheet
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\n\"Alignment\n\n
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\nCurated OER\n
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\nAlignment of a Solar Panel: Dot and Cross Products\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this dot and cross product worksheet, students identify vector points under given conditions determine vertical support and determine angles of an object. This two-page worksheet contains two problems.\n
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Worksheet
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\n\"Math\n\n
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\nCurated OER\n
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\nMath 224 Spring 2004: Dot Product\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this dot product activity, students consider two vectors and compute the dot product and cross product of the given vectors. This two-page activity contains four problems.\n
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eBook
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\n\"Calculus\n\n
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\nRice University\n
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\nCalculus Volume 3\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nSee calculus to the end. The eBook is the last of a three-volume series covering college-level calculus topics. Scholars begin with parametric equations and polar coordinates before moving to vectors, finally ending with multi-variable...\n
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Lesson Plan
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\n\"Worksheet\n\n
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\nCurated OER\n
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\nWorksheet 8 - Vectors\n

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\n\nFor Teachers\n\nHigher Ed\n
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\nIn 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...\n
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Instructional Video10:04
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\n\"Matrix\n\n
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\n3Blue1Brown\n
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\nMatrix Multiplication as Composition | Essence of Linear Algebra, Chapter 4\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nTake 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...\n
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Instructional Video14:12
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\n\"Dot\n\n
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\nDot Products and Duality | Essence of Linear Algebra, Chapter 7\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nThe 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...\n
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Lesson Plan
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\n\"May\n\n
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\nTeach Engineering\n
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\nMay the Magnetic Force Be with You\n

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\n\nFor Teachers\n\n10th - 12th\n\nStandards\n
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\nClass members use mathematics in order to better understand magnetic forces and their interaction on charged particles. After a demonstration of the interaction between a magnet and an electron beam using a CRT computer monitor,...\n
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Worksheet
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\n\"Worksheet\n\n
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\nCurated OER\n
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\nWorksheet 25- Spring 1996\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this math instructional activity, students find the values of the vectors. They also they prove that v and w are both orthogonal and find two nonparallel vectors.\n
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Worksheet
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\n\"Multivariable\n\n
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\nCurated OER\n
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\nMultivariable Calculus: Euclidean Geometry\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this Euclidean geometry activity, students determine if planes are parallel or perpendicular to each other. They identify the vector position. This two-page activity contains definitions, examples and explanations of how to do the...\n
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Instructional Video12:09
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\n\"Inverse\n\n
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\nInverse Matrices, Column Space and Null Space | Essence of Linear Algebra, Chapter 6\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nDetermine 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...\n
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Instructional Video10:59
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\n\"Linear\n\n
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\nLinear Transformations and Matrices | Essence of Linear Algebra, Chapter 3\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nAre 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...\n
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Handout
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\n\"Math\n\n
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\nMath Handbook: Trigonometry\n

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\n\nFor Students\n\n9th - 12th\n\nStandards\n
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\nYou'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...\n
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Instructional Video10:03
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\n\"The\n\n
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\n3Blue1Brown\n
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\nThe Determinant | Essence of Linear Algebra, Chapter 5\n

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\n\nFor Students\n\n11th - Higher Ed\n\nStandards\n
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\nDetermine 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...\n
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PPT
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\n\"Magnetic\n\n
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\nBowels Physics\n
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\nMagnetic Fields and Forces\n

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\n\nFor Teachers\n\n9th - 12th\n
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\nEvery knows that opposites attract! Here's a presentation that uses this background knowledge to explain magnetic fields and forces. The resource also explains the shape of magnetic fields and how to determine the direction of forces.\n
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PPT
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\n\"Torque:\n\n
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\nBowels Physics\n
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\nTorque: Rotational Statics and Rotational Dynamics\n

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\n\nFor Students\n\n9th - 12th\n
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\nScholars examine the application of torque in relation to motion by viewing a comprehensive presentation that explains the basic concepts related to torque and rotational motion. The lesson ends with examples showing how to calculate...\n
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Worksheet
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\n\"Worksheet\n\n
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\nCurated OER\n
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\nWorksheet 22\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn this math activity, students demonstrate that the point ( 1√ 2 , −1 2 , 1 2 ) lies on the unit sphere. They find the equation of the plane tangent to the unit sphere.\n
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Instructional Video
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\n\"Khan\n\n
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\nKhan Academy\n
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\nKhan Academy: Linear Algebra: Dot and Cross Product Comparison/intuition\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nVideo first reviews how to find the angle between two vectors, as well as restating the relationship between the cross product and the sine of that angle. Then gives an intuition of what the dot product and the cross product represent....\n
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Instructional Video
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\n\"Khan\n\n
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\nKhan Academy\n
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\nKhan Academy: Linear Algebra: Dot and Cross Product Comparison/intuition\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nVideo gives an intuition of what dot product and cross product represent. Also gives a comparison between cross product and dot product of vectors and how they are related. Shows which angles maximize the cross product and dot product....\n
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Instructional Video
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\n\"Khan\n\n
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\nKhan Academy\n
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\nKhan Academy: Linear Algebra: Cross Product Introduction\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nVideo explains the vector cross product and gives examples of finding it. Also discusses the usefulness and limitations of vector cross products and the differences from the dot product. [15:47]\n
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