• #### The Dot Product of Vectors - Problem 1

##### Math›Precalculus›Vectors and Parametric Equations
How to compute the dot product of two vectors, and how to demonstrate that the dot product is commutative.
• #### The Dot Product of Vectors - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to compute the dot product of two vectors, and how to demonstrate that the dot product distributes over addition.
• #### The Dot Product of Vectors - Concept

##### Math›Precalculus›Vectors and Parametric Equations
How to compute the dot product of two vectors.
• #### The Dot Product of Vectors - Problem 3

##### Math›Precalculus›Vectors and Parametric Equations
How to prove that the dot product uu of a vector with itself equals the square of its magnitude abs(u)^2.
• #### The Cross Product of Vectors - Problem 2

##### Math›Precalculus›Systems of Linear Equations and Matrices
How to show that the cross product of vectors u and v is perpendicular to both u and v.
• #### 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.
• #### Vector Operations in 3D - Concept

##### Math›Precalculus›Vectors and Parametric Equations
How to perform vector operations like addition, scalar multiplication, the dot product, and finding the magnitude, in three dimensions.
• #### The Angle Between Vectors - Concept

##### Math›Precalculus›Vectors and Parametric Equations
How to compute the angle between two vectors.
• #### The Angle Between Vectors - Problem 1

##### Math›Precalculus›Vectors and Parametric Equations
How to compute the angle between two vectors.
• #### The Angle Between Vectors - Problem 4

##### Math›Precalculus›Vectors and Parametric Equations
How to derive the formula for the angle between two vectors.
• #### The Angle Between Planes - Problem 1

##### Math›Precalculus›Vectors and Parametric Equations
How to determine if two planes are parallel or perpendicular.
• #### The Angle Between Vectors - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to determine whether two vectors are perpendicular or parallel.
• #### The Angle Between Vectors - Problem 3

##### Math›Precalculus›Vectors and Parametric Equations
How to compute one of the angles of a triangle when you are given the coordinates of its three vertices.
• #### The Angle Between Planes - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to find the angle between two planes.
• #### 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.
• #### The Angle Between Planes - Problem 3

##### Math›Precalculus›Vectors and Parametric Equations
How to find an equation of a plane parallel to or perpendicular to a given plane.
• #### 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.
• #### Vector Operations in 3D - Problem 2

##### Math›Precalculus›Vectors and Parametric Equations
How to find the angle between two vectors in three dimensions.
• #### Vector Operations in 3D - Problem 1

##### Math›Precalculus›Vectors and Parametric Equations
How to find the angle between two vectors in 3D, and how to tell whether two vectors are parallel or perpendicular.
• #### Perpendicular, Parallel and Skew Lines in Space - Problem 1

##### Math›Precalculus›Vectors and Parametric Equations
How to find the equation of a line parallel to and perpendicular to a given line in space.