Vectors & 3D Geometry in Spreadsheets: Dot & Cross Products, Planes & Projections

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Turn pairs of points in Kestrel Robotics' warehouse into vectors, measure their length, scale them to unit vectors and move a drone 4 m along one of them.
• Build the route of a Kestrel warehouse robot from scaled base moves, add the legs head to tail to get its positions, measure how far it ends from the start and plot the route from above.
• Compute dot products of six vector pairs from a Kestrel robot cell, turn them into the angle between the vectors with ACOS and DEGREES, and classify each angle as acute, right or obtuse.
• Calculate the work done by five forces with the dot product, the part of each force that acts along the motion, and split one force into its parallel and perpendicular parts.
• Compute the cross product of the two edges of five triangular shade sails with the component formula, take its length as the parallelogram area and order the sail fabric for the triangles.
• Build the equation of a sloped warehouse roof from three surveyed corners, find its tilt, and measure how far an antenna, a drone and other points are from the roof plane.
• Write two drone flight paths as parametric lines, tabulate their positions and separation over time, and find the exact time and distance of their closest approach.
• Compute the torque of a force on a robot wrist with the cross product, then shade the six faces of a 3D building model with Lambert's cosine law and chart how bright each face is.