production 12 videos

Product Rule of Logarithms
Precalculus Exponential and Logarithmic Functions
How to use the product rule for logarithms.
product rule of logarithms product rule 
The Dot Product of Vectors
Precalculus Vectors and Parametric Equations
How to compute the dot product of two vectors.
vector components component form dot product scalar product 
The Cross Product of Vectors
Precalculus Systems of Linear Equations and Matrices
How to compute the cross product of two 3D vectors.
unit vectors components cross product determinant 
Area With the Cross Product
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.
cross product magnitude of vectors dot product angle between vectors area parallelogram 
Vector Operations in 3D
Precalculus Vectors and Parametric Equations
How to perform vector operations like addition, scalar multiplication, the dot product, and finding the magnitude, in three dimensions.
vectors components vector addition scalar multiplication the dot product the scalar product magnitude length three dimensions 
Pascal's Triangle
Precalculus Topics in Discrete Math
How to use Pascal's triangle.
zero product property factoring constant 
Evaluating a Logarithmic Expression in terms of Known Quantities
Precalculus Exponential and Logarithmic Functions
How to break up a logarithm of a large number.
product rule of logs quotient rule of logs expand 
The Angle Between Vectors
Precalculus Vectors and Parametric Equations
How to compute the angle between two vectors.
dot product angle between vectors position vectors 
Addition and Scalar Multiplication of Vectors
Precalculus Vectors and Parametric Equations
How to compute the sum of two vectors or the product of a scalar and a vector.
vector components horizontal component vertical component component form vector addition the zero vector scalar multiplication 
Square Matrices
Precalculus Systems of Linear Equations and Matrices
How to determine whether two matrices can be multiplied, and if so, what the dimensions of the product will be.
matrices rows columns dimension matrix multiplication 
Perpendicular, Parallel and Skew Lines in Space
Precalculus Vectors and Parametric Equations
How to determine whether two lines in space are parallel or perpendicular.
perpendicular lines dot product direction vectors parallel lines scalar multiple skew lines 
The Angle Between Planes
Precalculus Vectors and Parametric Equations
How to find the angle between planes, and how to determine if two planes are parallel or perpendicular.
normal vector the angle between planes perpendicular planes dot product scalar multiple parallel planes