# Calculus III

Here you will find 60+ Calculus III videos that cover every main concept you will see in a typical Calculus III class. Scroll through the gallery below which is sorted in order of topics as they are typically addressed throughout the semester.

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## Topics Covered

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- Vector Basics
- Component Form
- Line Segment to Component Form
- Line Segment to Component Form – Example 1
- Line Segments vs Component Form – Example 2
- Scalar Multiplication
- Adding and Subtracting Vectors
- Vector Operations – Example 1
- Standard Unit Vectors
- Magnitude of a Vector
- Magnitude of a Vector – Example 1
- Unit Vector
- How to Normalize a Vector
- Using Angles to Write Vectors
- Using an Angle to Write a Vector – Example 1
- Resultant Force Vectors
- 3D Vectors
- Colinear Points – Example 1
- Vector Dot Product
- Dot Product – Example 1
- Using Dot Product to Find the Angle Between Two Vectors
- Finding Angles Using Dot Products – Example 1
- Using Dot Products to Find Angles Between Vectors – Example 2
- Finding Angles Within a Triangle Using Calculus

- Vector Projections
- Vector Projections – Example 1
- Vector Projection Application – Rolling Cart
- Vector Cross Product
- Vector Cross Product – Example 1
- Vector Cross Product – Extra Theory
- Lines in Space
- Lines in Space – Example 1
- Lines in Space – Example 2
- Symmetric Equations – Lines in Space
- Line in Space – Parametric to Symmetric, Example 1
- Lines in Space – Symmetric to Parametric, Example 2
- Are These Lines in Space Parallel? – Example 3
- Equations of Planes in Space
- Plane in Space – Extra Theory
- Standard vs General Form of a Plane
- Normal Vector of a Plane
- Equation of a Plane – Example 1, easy
- Equation of a Plane Given 3 Points – Example 2, medium
- Equation of a Plane Given a Line in the Plane – Example 3, medium
- Distance Between Point and Plane
- Distance Between Point and Plane – Example 1
- Distance Between a Point and a Line

- Distance Between a Point and a Line – Example 1
- Angle Between Two Planes
- Angle Between Two Planes – Example 1
- Line of Intersection of Two Planes
- Cylindrical Coordinates in Space
- Spherical Coordinates in Space
- Cylindrical and Spherical Conversions
- Rectangular to Cylindrical Conversion – Example 1
- Rectangular to Cylindrical Conversion – Example 2
- Cylindrical to Rectangular Conversion – Example 3
- Cylindrical to Rectangular Conversion – Example 4
- Rectangular to Spherical Conversion – Example 5
- Rectangular to Spherical Conversion – Example 6
- Spherical to Rectangular Conversion – Example 7
- Spherical to Rectangular Conversion – Example 8
- Curvature Example (Calculus III)
- Triple Int Rewrite Example
- Triple Integral Ex Mass2

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Vector Basics

Component Form

Line Segment to Component Form

Line Segment to Component Form - Example 1

Line Segments vs Component Form - Example 2

Scalar Multiplication

Adding and Subtracting Vectors

Vector Operations - Example 1

Standard Unit Vectors

Magnitude of a Vector

Magnitude of a Vector - Example 1

Unit Vector

How to Normalize a Vector

Using Angles to Write Vectors

Using an Angle to Write a Vector - Example 1

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