Khan Academy: Defining a Plane in R3 With a Point and Normal Vector

Video shows how to define a plane in R3 using a point on the plane and a normal vector to the plane. Includes a visual representation to help understanding. [13:53]

Video shows how to define a plane in R3 using a point on the plane and a normal vector to the plane. Includes a visual representation to help understanding. [13:53]

Video shows how to write a transformation matrix in R^3 that rotates a vector around the x-axis. Compares the rotation matrix in R^3 to the rotation matrix in R^2 found in the previous video and discusses how it could be applied for more...

Video reviews how to find a basis for the column space and talks about how to find it more efficiently using reduced row echelon form. Shows a visualization of the column space in R3 as a plane. Shows two methods to determine the...

This video demonstrates how to take linear equations written in either slope-intercept form or point-slope form and rewrite them in standard form of a linear equation. Right-click on the square at the bottom right for a full-screen view....

This video gives several examples of how to write a linear equation in point-slope form given two points on the line. This video is also found in the strand Algebra: ck12.org. [9:38]

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...

Video defining a specific orthonormal basis and using the simplified formula found in the previous video to calculate the projection of a vector onto a subspace with the given orthonormal basis. [6:42]

Video giving another reason why orthonormal bases are useful. First reviews how to find the projection of a vector onto a subspace and then describes how an orthonormal basis can be used to find the projection. Simplifies the...

Video using the Gram-Schmidt process to create an orthonormal basis from a specific basis with three basis vectors in four-dimensional space. [13:57]