• The Angle Between Planes - Concept

Math›Precalculus›Vectors and Parametric Equations
How to find the angle between planes, and how to determine if two planes are parallel or perpendicular.
• Perpendicular, Parallel and Skew Lines in Space - Concept

Math›Precalculus›Vectors and Parametric Equations
How to determine whether two lines in space are parallel or perpendicular.
• Introduction to the 3D Coordinate System - Problem 1

Math›Precalculus›Vectors and Parametric Equations
How to find the coordinates of the vertices of a rectangular box.
• The Angle Between Planes - Problem 2

Math›Precalculus›Vectors and Parametric Equations
How to find the angle between two planes.
• The Midpoint and Distance Formulas in 3D - Problem 1

Math›Precalculus›Vectors and Parametric Equations
How to find the length and midpoint of a segment in three dimensions.
• Introduction to Planes - Problem 2

Math›Precalculus›Vectors and Parametric Equations
How to graph a plane by plotting its intercepts.
• Navigation Problems - Problem 1

Math›Precalculus›Vectors and Parametric Equations
How we find the course and groundspeed of an airplane when we are given its velocity and the wind velocity.
• Navigation Problems - Problem 2

Math›Precalculus›Vectors and Parametric Equations
How we find the course and groundspeed of a complicated airplane problem when we are given its velocity and the wind velocity at 210 and 270 degrees.
• Navigation Problems - Problem 3

Math›Precalculus›Vectors and Parametric Equations
How we find the course and groundspeed of an airplane when we are given its velocity and the wind velocity.
• Introduction to Planes - Problem 1

Math›Precalculus›Vectors and Parametric Equations
How to write an equation for planes that contain one of the sides of a rectangular box.
• Introduction to Planes - Concept

Math›Precalculus›Vectors and Parametric Equations
How to write an equation for the coordinate planes or any plane that is parallel to one.
• The Midpoint and Distance Formulas in 3D - Problem 4

Math›Precalculus›Vectors and Parametric Equations
How to find the center and radius of a sphere when its equation is not in center-radius form by completing the square.
• The Cross Product of Vectors - Problem 1

Math›Precalculus›Systems of Linear Equations and Matrices
How to show that when you reverse the order of a cross product, you get the opposite result.
• Area With the Cross Product - Concept

Math›Precalculus›Systems of Linear Equations and Matrices
How to show that the magnitude of the cross product of two vectors gives the area of the parallelogram determined by those two vectors.
• Area With the Cross Product - Problem 1

Math›Precalculus›Systems of Linear Equations and Matrices
How to compute the area of a parallelogram using the cross product of the vectors that determine it.
• Area With the Cross Product - Problem 3

Math›Precalculus›Systems of Linear Equations and Matrices
How to compute the area of a triangle in xyz-space using vectors formed from two of its sides.
• Area With the Cross Product - Problem 2

Math›Precalculus›Systems of Linear Equations and Matrices
How to compute the area of a triangle in the xy-plane using vectors formed from two of its sides.
• Area With Determinants - Concept

Math›Precalculus›Systems of Linear Equations and Matrices
How to compute the area of a parallelogram using a determinant.
• Area With Determinants - Problem 1

Math›Precalculus›Systems of Linear Equations and Matrices
How to compute the area of a triangle using a determinant.
• Area With Determinants - Problem 3

Math›Precalculus›Systems of Linear Equations and Matrices
How to compute the area of an irregular quadrilateral using determinants.