Vectors & 3D Geometry in Spreadsheets: Dot & Cross Products, Planes & Projections
Build 3D vectors from points, measure lengths and unit vectors, add and scale displacements and chart a route, find angles with the dot product, project forces and compute work, take cross products for areas, build a plane from three points and measure distances to it, find the closest approach of two drones and finish with torque and cosine shading: 8 graded labs with SUMPRODUCT, SUMSQ, ACOS and plain component formulas.
The first lesson is free — no account needed.
About this course
A vectors and 3D geometry course that solves the geometry problems of one fictional robotics company, Kestrel Robotics, in a spreadsheet, for high school and university students in maths, physics and engineering, game and graphics developers and anyone revising linear algebra. You build vectors from points and calculate lengths and unit vectors with SUMSQ, add scaled moves head to tail and chart a robot's route, find the angle between vectors with SUMPRODUCT, ACOS and DEGREES, project forces onto the motion and compute work, take cross products with the component formula for parallelogram and triangle areas, build the equation of a plane from three points and measure the distance of a point to it, find the closest approach of two drones on parametric lines, and finish with torque and Lambert cosine shading. Fictional company and illustrative numbers. The first lab is free.
Lessons
- Vector Components, Length & Unit Vectors in 3DFree
- Vector Addition & Scalar Multiples: a Robot's Route (Chart) Pro
- Dot Product & the Angle Between 3D Vectors (ACOS, DEGREES) Pro
- Projections & Work: Force · Displacement Pro
- Cross Product & Area: Parallelograms and Triangles (No MMULT) Pro
- Plane from Three Points & Distance from a Point to a Plane Pro
- Lines in 3D: Parametric Form & Closest Approach of Two Drones Pro
- Applications: Torque (r × F) & Cosine Shading with Normals (Chart) Pro