Chapter 11 Videos
11.1: Vectors in the Plane
- Video (David): Review of vector addition and scaling from 2D space
- Video (Patrick) (Optional): Finding components given magnitude and angle.
- Video (Patrick) (Optional): Adding and scaling vectors geometrically
- Video (Patrick) (Optional): Adding and scaling vectors component-wise
- Video (Patrick) and Part 2: Finding unit vectors.
11.2: Rectangular Coordinates in 3D
- Video (David): Intro to 3D space and right-hand rule
- Video (David): The coordinate planes
- Video (David): Distance formula
- Video (David): Equation of a sphere in 3D space
11.3: Vectors in 3D
- Video (David): Vectors in 3D space
11.4: Dot Product
- Video (David): Dot product in component form
- Video (David): Dot product in geometric form, finding angle between vectors
- Video (David) (optional): Proof that the component and geometric forms of the dot product are equivalent
- Video (Patrick) (optional): Dot product component and geometric forms, finding angle between vectors, determining if two vectors are orthogonal.
- Video (James): Finding the projection of one vector onto another.
- Video (James) (optional): The derivation of the projection equations.
- Video (James) (optional): An application of the dot product to calculating work
11.5: Cross Product
- Video (James): Calculating the cross product using the determinant method, and additional properties.
- Video (Patrick) (optional): Computing the cross product
- Video (David): Finding the area of a parallelogram using the cross product
- Video (James) (optional): An application of the cross product to finding torque
- Video (Khan) (optional): A comparison between the dot and cross product
- Video (James) (optional): Finding the volume of a parallelpiped using the scalar triple product.
11.6: Lines and Planes in 3D
- Video (David): The vector and parametric equations of a line in 3D space
- Video (David): Finding the equation of a line through 2 points.
- Video (Patrick) (optional): Finding the vector equation of a line through 2 points. Can skip to 2:30 for the examples.
- Video (James) (optional): The parametric equations of a line in 3D space. This video also discuss the “symmetric equation of a line” which we will not be covering.
- Video (David): Determine if two lines are parallel, skew, or intersect. "Skew" is a way of saying the lines are not parallel and do not intersect.
- Video (David): Deriving the standard equation of a plane
- Video (James): The standard equation of the plane, with examples of finding an equation given a point and normal vector, and given 3 points.
- Video (Patrick) (optional): Finding an equation for a plane through 3 points.
- Video (Patrick): Finding the intersection of a line and plane.
- Video (James) (optional): Graphing planes using traces
- Video (James): Finding the angle between planes.
- Video (David): Finding an equation of a plane given a line and a point. Finding an equation of a plane parallel to another.