Explore vectors in 3D space through a comprehensive video lecture covering Stewart Calculus Chapter 12. Learn about points in 3D space, distance formulas, and spherical equations with practical examples. Discover how to calculate distances from points to axes, determine unit vectors, and assess vector parallelism. Delve into vector operations, including magnitude, resultant forces, and tension calculations in static equilibrium scenarios. Master the dot product concept and its applications in finding angles between vectors and perpendicular unit vectors. Apply vector knowledge to real-world problems involving torque and force calculations. Investigate the relationships between intersecting lines and planes in 3D, including parallel and orthogonal configurations. Conclude by learning to determine acute angles between lines and planes, providing a solid foundation in 3D vector mathematics.
Overview
Syllabus
Introduction to Points in 3 Dimensional Space.
Distance Formula and Equation of a Sphere in 3D With Examples.
Distance from a Point to the y-axis in 3D Space..
Find a Unit Vector in the Same Direction as the Given Vector.
Are the two Vectors Parallel? :: How to Determine if Vectors are Parallel.
Magnitude and Angle of the Resultant Force :: Cartesian Components of Vectors.
Find the Tension in Cables Attached to a Hanging Mass:: Vectors :: Static Equillibrium.
Dot Product of Two Vectors.
How to Find the Angle Between Two Vectors :: Why Cosine and Dot Product Explained.
Find Unit Vector Perpendicular to Two Vectors :: Using Dot Product!.
Find Force Needed to Supply 100 Nm of Torque.
Angle Between two Intersecting Lines :: 3D Vectors :: First Show Intersection.
Planes Parallel, Orthogonal, or Neither, Angle Between Planes Approach.
Acute Angle Between a Line and a Plane.
Taught by
Jonathan Walters
