Calculus 3 - Vector Projections & Orthogonal Components

This calculus 3 video tutorial explains how to find the vector projection of u onto v using the dot product and how to find the vector component of u orthogonal to v. W1 is the component of u parallel to v and w2 is the component of u perpendicular to v.

3D Coordinate System:

3D Distance Formula:

Equation of a 3D Sphere:

Calculus 3 - Intro to Vectors:

Calculus 3 - The Dot Product:

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Angle Between Two Vectors:

Parallel & Orthogonal Vectors:

Direction Cosines and Vectors:

Calculus 3 - Vector Projections:

Cross Product of 2 Vectors:

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Area - Vector Cross Product:

Triple Scalar Product:

Vector Equations of Lines:

The Equation of a Plane:

Planar Equation - 3 Points:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

Vectors - Free Formula Sheet:

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Also a way to check would be to verify that either “W2” dot V =0. That just proves again that they are perpendicular to each other. 1st example, W2 dot V = (2/5*10/5+(-1/5)*20/5)=0 any other answer means there is an error somewhere.

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Professor Organic Chemistry Tutor, thank you for another excellent video/lecture on Vector Projections and Orthogonal Components in Calculus Three. Vector Projections and Orthogonal Components are also used in Engineering Electromagnetics and Engineering Physics. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

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