{"results":"
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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: Relationship Between Cross Product and Angle Sin\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nVideo proving that the magnitude of the cross product of two vectors is equal to the product of their magnitudes and the sine of the angle between them. [18:09]\n
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\n\nGet Free Access\n\nSee Review\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: Dot and Cross Product Comparison/intuition\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nThis video 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.\n
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\n\nGet Free Access\n\nSee Review\n
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Unit Plan
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\n\"Ck\n\n
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\nCK-12 Foundation\n
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\nCk 12: Analysis: Cross Products\n

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\n\nFor Students\n\n11th - 12th\n
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\n[Free Registration/Login may be required to access all resource tools.] In this lessons students will be defining and calculating cross products and normal vectors. Students examine guided notes, review guided practice, watch...\n
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\n\nGet Free Access\n\nSee Review\n
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Instructional Video
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\n\"Sophia:\n\n
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\nSophia Learning\n
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\nSophia: Finding the Cross Product of Vectors: Lesson 3\n

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\n\nFor Students\n\n9th - 10th\n
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\nThis lesson demonstrates how the cross product of two vectors is found. It is 3 of 9 in the series titled \"Finding the Cross Product of Vectors.\"\n
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\n\nGet Free Access\n\nSee Review\n
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Instructional Video
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\n\"Sophia:\n\n
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\nSophia Learning\n
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\nSophia: Finding the Cross Product of Vectors: Lesson 4\n

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\n\nFor Students\n\n9th - 10th\n
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\nThis lesson demonstrates how the cross product of two vectors is found. It is 4 of 9 in the series titled \"Finding the Cross Product of Vectors.\"\n
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\n\nGet Free Access\n\nSee Review\n
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Instructional Video
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\n\"Sophia:\n\n
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\nSophia Learning\n
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\nSophia: Finding the Cross Product of Vectors: Lesson 8\n

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\n\nFor Students\n\n9th - 10th\n
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\nThis lesson demonstrates how the cross product of two vectors is found. It is 8 of 9 in the series titled \"Finding the Cross Product of Vectors.\"\n
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\n\nGet Free Access\n\nSee Review\n
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Instructional Video
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\n\"Sophia:\n\n
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\nSophia Learning\n
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\nSophia: Finding the Cross Product of Vectors: Lesson 5\n

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\n\nFor Students\n\n9th - 10th\n
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\nThis lesson demonstrates how the cross product of two vectors is found. It is 5 of 9 in the series titled \"Finding the Cross Product of Vectors.\"\n
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\n\nGet Free Access\n\nSee Review\n
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Unit Plan
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\n\"University\n\n
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\nUniversity of Nebraska\n
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\nUniversity of Nebraska: The Cross Product\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nThis resource provides a definition and demonstration of the cross product.\n
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\n\nGet Free Access\n\nSee Review\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: Calculating Dot and Cross Products With Unit Vector Notation\n

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\n\nFor Students\n\n11th - 12th\n\nStandards\n
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\nCalculating the dot and cross products when vectors are presented in their x, y, and z (or i, j, and k) components. [9:46]\n
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\n\nGet Free Access\n\nSee Review\n
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\n\"Khan\n\n
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\nKhan Academy\n
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\nKhan Academy: Electricity and Magnetism: Cross Product 1\n

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\n\nFor Students\n\n11th - 12th\n
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\nA video lecture that introduces how to do the cross product. Understand how crossing two vectos produces a third vector. [10:03]\n
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\n\nGet Free Access\n\nSee Review\n
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\nKhan Academy\n
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\nKhan Academy: Electricity and Magnetism: Cross Product 2\n

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\n\nFor Students\n\n9th - 10th\n
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\nVideo lecture provides a little more intuition on the cross product. [10:53]\n
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\n\nGet Free Access\n\nSee Review\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: Vector Dot and Cross Products: Normal Vector From Plane Equation\n

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\n\nFor Students\n\n9th - 10th\n
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\nVideo finding the normal vector to a plane using its equation by first visualizing the vector and the plane and then solving for it.\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: Electricity & Magnetism: Dot & Cross Products\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nCalculating the dot and cross products when vectors are presented in their x, y, and z (or i, j, and k) components. [9:47]\n
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\n\nGet Free Access\n\nSee Review\n
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\n\"Khan\n\n
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\nKhan Academy\n
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\nKhan Academy: Moments, Torque, and Angular Momentum: Cross Product and Torque\n

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\n\nFor Students\n\n9th - 10th\n
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\nLearn how to find the direction component of torque with this video. Review vector quantities to understand how to apply the right hand rule to a torque problem. [10:00]\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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\n\nGet Free Access\n\nSee Review\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 its differences from the dot product. [15:47]\n
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\n\nGet Free Access\n\nSee Review\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: Relationship Between Cross Product and Angle Sin\n

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\n\nFor Students\n\n9th - 10th\n
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\nVideo showing proof of the relationship between cross product and sin. [18:09]\n
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\n\nGet Free Access\n\nSee Review\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: Vector Triple Product Expansion (Very Optional)\n

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\n\nFor Students\n\n9th - 10th\n
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\nVideo deriving the triple product expansion by expanding the cross product of 3 vectors and then simplifying it to the difference of dot products.\n
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\n\nGet Free Access\n\nSee Review\n
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Handout
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\n\"Wolfram\n\n
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\nWolfram Research\n
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\nWolfram Math World: Cross Product\n

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\n\nFor Students\n\n9th - 10th\n
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\nThis site from Mathworld.com contains an explanation of a croos product and example with links to clarify unfamiliar proceedures in finding a cross product. If you are not famialiar with the right-hand rule, be sure to go click on the...\n
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\n\nGet Free Access\n\nSee Review\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: Vector Triple Product Expansion (Very Optional)\n

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\n\nFor Students\n\n9th - 10th\n
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\nVideo deriving the triple product expansion by expanding the cross product of 3 vectors and then simplifying it to the difference of dot products. [14:25]\n
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\n\nGet Free Access\n\nSee Review\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: Vector Dot and Cross Products: Vector Triangle Inequality\n

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\n\nFor Students\n\n9th - 10th\n
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\nThi videoreviews the Cauchy-Schwarz inequality and then shows a proof of the triangle inequality for vectors and relates it to the triangle inequality from 2-dimensional geometry.\n
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\n\nGet Free Access\n\nSee Review\n
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Activity
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\n\"Paul's\n\n
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\nPaul Dawkins\n
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\nPaul's Online Notes: Calculus Ii: Vectors\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nThe 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...\n
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Instructional Video
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\n\"Sophia:\n\n
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\nSophia Learning\n
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\nSophia: Cross Product\n

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\n\nFor Students\n\n9th - 10th\n
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\nThis lesson introduces the cross product\n
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\n\nGet Free Access\n\nSee Review\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: Vector Dot and Cross Products: Cross Product Introduction\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nThis video ha an introduction to the cross productand gives examples of finding it.\n
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\n\nGet Free Access\n\nSee Review\n
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