# 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.