scalar quantities 18 videos

Vector Quantities  Scalar Quantities
Physics Linear and Projectile Motion
Understanding the differences between vectors and scalar quantities.
vector scalar quantities magnitude direction 
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 
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 
Evaluating a Logarithmic Expression in terms of Known Quantities
Algebra 2 Inverse, Exponential and Logarithmic Functions
How to break up a logarithm of a large number.
product rule of logs quotient rule of logs expand 
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 

Matrix Operations
Algebra 2 Matrices
How to use simple matrix operations.
adding matrices scalar multiple matrix matrices 
Augmented Matrices
Algebra 2 Matrices
How to use matrices to solve a system of linear equations.
augmented matrix row operations scalar multiple 
Mixture Problems
Algebra Word Problems Using Systems of Equations
How to solve word problems when mixing two quantities with different prices.
amount price mixture word problem 
Definite Integrals As Net Change
Calculus The Definite Integral
How to use the fundamental theorem of calculus to compute the net change of a quantity.
definite integral net change rate of change net change theorem fundamental theorem of calculus 
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 
Instantaneous Rate of Change
Calculus The Derivative
How to estimate the instantaneous rate liquid is pouring out of a container at t=4 by computing average rates of change over shorter and shorter intervals of time.
average rate of change instantaneous rate of change change in quantity change in time limits 
The Geometric Representation of Vectors
Precalculus Vectors and Parametric Equations
How to understand what vectors are, and how they can be represented geometrically.
Magnitude Direction Scalar Vector Directed Line Segment Initial Point Terminal Point 
Unit Vectors
Precalculus Vectors and Parametric Equations
How to express a vector algebraically in terms of the unit vectors i and j.
unit vectors length magnitude the unit vectors i and j vector addition scalar multiplication component form 
The Vector Equation of a Line
Precalculus Vectors and Parametric Equations
How to write the vector equation of a line.
position vector direction vector vector addition scalar multiple vector equation line 
The Midpoint and Distance Formulas in 3D
Precalculus Vectors and Parametric Equations
How to derive the formula for the midpoint of a segment in three dimensions.
position vectors the vector from point a to point b the midpoint formula vector addition scalar 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