The Dot Product, Vectors & Projection
A 12-part course with Math Fortress
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- Total Time 1 hr, 49 min
- Lessons 12
- Exercises 28
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62 CQ
12 Lessons in This Course
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11 minCalculus lesson 16 CQ
In this advanced calculus lesson, get introduced to the dot product, also known as the scalar product, and review how scalar multiplication works.
with Math FortressIn this advanced calculus lesson, get introduced to the dot product, also known as the scalar product, and review how scalar multiplication works.
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8 minCalculus lesson 25 CQ
In this second calculus lesson on dot products, learn how to derive another method to compute the dot product between two vectors, and run through properties.
with Math FortressIn this second calculus lesson on dot products, learn how to derive another method to compute the dot product between two vectors, and run through properties.
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8 minCalculus lesson 35 CQ
In this calculus lesson, go over several examples illustrating how to solve problems that make use of the geometric and component definition of the dot product.
with Math FortressIn this calculus lesson, go over several examples illustrating how to solve problems that make use of the geometric and component definition of the dot product.
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8 minCalculus lesson 45 CQ
In this level four dot product calculus lesson, run through five example problems for solving dot product issues, including finding perpendicular vectors.
with Math FortressIn this level four dot product calculus lesson, run through five example problems for solving dot product issues, including finding perpendicular vectors.
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10 minCalculus lesson 56 CQ
In this advanced calculus lesson, continue practicing dot product problems, and in particular, learn how to find the angle between two vectors.
with Math FortressIn this advanced calculus lesson, continue practicing dot product problems, and in particular, learn how to find the angle between two vectors.
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11 minCalculus lesson 66 CQ
Are the given vectors orthogonal, parallel, or neither? In this advanced calculus lesson, run through practice problems that require the use of the dot product.
with Math FortressAre the given vectors orthogonal, parallel, or neither? In this advanced calculus lesson, run through practice problems that require the use of the dot product.
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10 minCalculus lesson 76 CQ
In this advanced calculus lesson, run through three challenging problems that require use of the dot product, including finding points of intersection.
with Math FortressIn this advanced calculus lesson, run through three challenging problems that require use of the dot product, including finding points of intersection.
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8 minCalculus lesson 85 CQ
Time to make use of the dot product with this application. Learn about scalar projections, vector projections, and orthogonal projections in this math lesson.
with Math FortressTime to make use of the dot product with this application. Learn about scalar projections, vector projections, and orthogonal projections in this math lesson.
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5 minCalculus lesson 93 CQ
In this calculus lesson, discover the dot product (or the scalar product) and follow along with examples covering scalar, vector, and orthogonal projection.
with Math FortressIn this calculus lesson, discover the dot product (or the scalar product) and follow along with examples covering scalar, vector, and orthogonal projection.
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8 minCalculus lesson 105 CQ
Continue discussing the dot product in this calculus lesson reviewing direction angles and direction cosines, and practice rewriting expressions for magnitude.
with Math FortressContinue discussing the dot product in this calculus lesson reviewing direction angles and direction cosines, and practice rewriting expressions for magnitude.
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10 minCalculus lesson 116 CQ
In this multivariable calculus lesson, get introduced to an uncommon definition of "work." Learn how to find the work done by a constant force.
with Math FortressIn this multivariable calculus lesson, get introduced to an uncommon definition of "work." Learn how to find the work done by a constant force.
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7 minCalculus lesson 124 CQ
In this multivariable calculus lesson, learn how to solve proofs using the Cauchy-Schwarz inequality, triangle inequality, and the parallelogram law.
with Math FortressIn this multivariable calculus lesson, learn how to solve proofs using the Cauchy-Schwarz inequality, triangle inequality, and the parallelogram law.
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35258 min35-part Geometry course146 CQ
Having trouble in geometry class? Reviewing for the SATs? This course from Math Fortress explains the principles of geometry, from segments, intersections, and degrees to angles and congruence.
with Math FortressHaving trouble in geometry class? Reviewing for the SATs? This course from Math Fortress explains the principles of geometry, from segments, intersections, and degrees to angles and congruence.
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1293 min12-part Algebra course54 CQ
New to algebra and confused by its concepts? In this Algebra I course for beginners, Math Fortress provides clear and concise explanations, starting with variables and ending with word problems.
with Math FortressNew to algebra and confused by its concepts? In this Algebra I course for beginners, Math Fortress provides clear and concise explanations, starting with variables and ending with word problems.
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13119 min13-part Algebra course66 CQ
Now that you have algebra basics down, it's time to delve into quadratic equations. In this math course, students learn how to solve binomial and trinomial quadratic equations through factoring.
with Math FortressNow that you have algebra basics down, it's time to delve into quadratic equations. In this math course, students learn how to solve binomial and trinomial quadratic equations through factoring.
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981 min9-part Calculus course45 CQ
Calculating derivatives can be tricky if you aren't comfortable with differential calculus. In this course, learn how to find the derivatives of polynomials, natural exponential functions, and more.
with Math FortressCalculating derivatives can be tricky if you aren't comfortable with differential calculus. In this course, learn how to find the derivatives of polynomials, natural exponential functions, and more.
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13103 min13-part Calculus course59 CQ
Know the basics of differentiation, and feel ready to learn more intermediate-level calculus? In this course, Math Fortress presents integration techniques to find the integrals of functions.
with Math FortressKnow the basics of differentiation, and feel ready to learn more intermediate-level calculus? In this course, Math Fortress presents integration techniques to find the integrals of functions.
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1183 min11-part Calculus course47 CQ
Need some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
with Krista King MathNeed some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
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10129 min10-part Math course70 CQ
Statistics may sound like a dry topic, but developing data analysis skills will unlock fascinating worlds! In this 10-lesson course from statistics teacher Zac Rappell, start by understanding group data and central tendencies (mean, median, and mode), then explore measures of spread (range, IQR, and standard deviation). Learn how to create stem and leaf and box and whisker plots, and practice comparing data sets to identify new relationships. Finish with a fun final project analyzing the Oscars!
with Zachary RappellStatistics may sound like a dry topic, but developing data analysis skills will unlock fascinating worlds! In this 10-lesson course from statistics teacher Zac Rappell, start by understanding group data and central tendencies (mean, median, and mode), then explore measures of spread (range, IQR, and standard deviation). Learn how to create stem and leaf and box and whisker plots, and practice comparing data sets to identify new relationships. Finish with a fun final project analyzing the Oscars!
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31113 min31-part Algebra course73 CQ
Studying for the Regents Exam and need help with the algebra one section? In this course, run through thirty-seven example problems that cover basic algebra concepts you'll need to know to pass.
with Math FortressStudying for the Regents Exam and need help with the algebra one section? In this course, run through thirty-seven example problems that cover basic algebra concepts you'll need to know to pass.
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993 min9-part Calculus course51 CQ
Calculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
with Math FortressCalculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
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630 min6-part Math course17 CQ
Fundamentals of Laplace transforms such as definition, limits, properties, and few examples.
with Anish TurlapatyFundamentals of Laplace transforms such as definition, limits, properties, and few examples.
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1183 min11-part Calculus course47 CQ
Need some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
with Krista King MathNeed some tips for Calculus 1A? Or maybe you’re madly reviewing for tomorrow's math test? Either way, never fear - Krista, an experienced math tutor, will help you understand the world of calculus, step-by-step. Start by learning the difference between a function and an equation - and how to analyze a function's graph for continuity and limits. Then, step into the world of tangent lines, differentiation, and more. Each lesson includes examples and sample problems to help you along the way.
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10133 min10-part Calculus course72 CQ
Worried about taking a college-level or AP Calculus class? Fret not! In this course, review simple examples and graphs to explore the main concepts of both differential and integral calculus.
with Math is a SportWorried about taking a college-level or AP Calculus class? Fret not! In this course, review simple examples and graphs to explore the main concepts of both differential and integral calculus.
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10110 min10-part Calculus course59 CQ
Do you need a little help preparing for the AP Calculus AB exam? Look no further. This course covers the basic ideas of calculus, including: functions, limits, derivatives, and integration.
with Mark HuberDo you need a little help preparing for the AP Calculus AB exam? Look no further. This course covers the basic ideas of calculus, including: functions, limits, derivatives, and integration.
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993 min9-part Calculus course51 CQ
Calculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
with Math FortressCalculus students ready to advance to the next level: this course is for you. Learn all about the cross product, starting with the right hand rule, and ending with how to measure torque.
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12109 min12-part Calculus course62 CQ
In this calculus course discover the geometric interpretation of the dot product (also known as the scalar product), the component definition of the dot product, and properties of the dot product.
with Math FortressIn this calculus course discover the geometric interpretation of the dot product (also known as the scalar product), the component definition of the dot product, and properties of the dot product.