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Curated Video
Vector Dot Product
Understand how the dot product of two vectors yields a scalar quantity and how scalar multiplication affects vector direction and magnitude. Explore the formula, geometric meaning, and unit vector method to calculate dot products in...
Math Fortress
Calculus III: The Dot Product (Level 9 of 12)
This video goes over the dot product also known as the scalar product. This video goes over 3 examples illustrating how to find the scalar projection, vector projection, and orthogonal projection.
Math Fortress
Calculus III: The Dot Product (Level 8 of 12)
This video goes over the dot product also known as the scalar product. This video covers an application of the dot product specifically, the scalar projection, vector projection, and orthogonal projection.
Khan Academy
Khan Academy: Linear Algebra: Introduction to Projections
Video reviews how to use vectors to define a line. Gives an intuitive sense of what a projection is, then explains step-by-step where the formula for projections comes from. Shows an example of calculating a vector projection. [14:37]
Khan Academy
Khan Academy: Linear Algebra: Projections Onto Subspaces
A video lesson defining projections onto subspaces. Uses the definition for a projection onto a line and then shows that a generalized version of the formula works for a projection onto any subspace. Includes a concrete example and...
Khan Academy
Khan Academy: Linear Algebra: Expressing Projection as Matrix Vector Product
Video shows how to simplify the vector projection formula using unit vectors. Shows that projections are linear transformations. Shows the general formula for the transformation matrix for projections in R^2. Shows an example using the...
Khan Academy
Khan Academy: Linear Algebra: Expressing Projection as Matrix Vector Product
Video shows how to simplify the vector projection formula using unit vectors. Shows that projections are linear transformations. Shows the general formula for the transformation matrix for projections in R^2. Shows an example using the...
Khan Academy
Khan Academy: Linear Algebra: Dot and Cross Product Comparison/intuition
Video 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....
Khan Academy
Khan Academy: Linear Algebra: Introduction to Projections
Video reviews how to use vectors to define a line. Gives an intuitive sense of what a projection is then explains step by step where the formula for projections comes from. Shows example of calculating vector projections. [14:37]