Vectors & Coordinate Geometry

11 interactive Mathematics simulations on vectors & coordinate geometry.

Conic sections by eccentricity Mathematics · Vectors & Coordinate Geometry With the same focus and directrix, only the eccentricity e changes: e < 1 gives an ellipse, e = 1 a parabola, e > 1... Ages 15–16
Vector addition – tip-to-tail and parallelogram rules Mathematics · Vectors & Coordinate Geometry Drag vectors from the tray onto a coordinate grid and build the resultant using the tip-to-tail (triangle) rule or... Ages 15–16
Conic sections – the reflective property (satellite dish, whispering gallery, telescope) Mathematics · Vectors & Coordinate Geometry Rays of light hit a mirror shaped like a conic section and you watch where they go after reflecting: rays parallel... Ages 15–16
Lines and circles in the coordinate plane Mathematics · Vectors & Coordinate Geometry Line Δ: ax + by + c = 0 has normal vector n = (a; b) and direction vector u = (−b; a) drawn right on the figure;... Ages 15–16
2 × 2 matrices as transformations – determinant, composition, inverse and eigenvectors Mathematics · Vectors & Coordinate Geometry Edit a 2 × 2 matrix, or drag the images of the two unit vectors, and watch the unit square and a shape (letter F,... Ages 16–17
2D + 3D Planes and spheres in 3D space – distance from center to plane Mathematics · Vectors & Coordinate Geometry In a rotatable Oxyz coordinate system, the plane (P): Ax + By + Cz + D = 0 and a sphere with center I and radius R... Ages 17–18
Coordinate Plane – Four Quadrants, Reflections and Distances Mathematics · Vectors & Coordinate Geometry Drag two points A and B on the coordinate plane to read their coordinates, signs and quadrant; reflect A in the x-... Ages 13–14
Geometric Transformations and Composition Mathematics · Vectors & Coordinate Geometry Drag the F-shape and the elements of each transformation (translation vector, center of rotation, line of... Ages 16–17
2D + 3D Vector equations of lines in 3D – intersecting, parallel and skew lines Mathematics · Vectors & Coordinate Geometry A line r = a + λb in a rotatable 3D coordinate frame (2D projection or 3D view): drag the point P(λ) along the line... Ages 17–18
Vectors – sum, difference, scalar multiple and dot product Mathematics · Vectors & Coordinate Geometry Two vectors u, v are drawn from the origin O on a coordinate grid; students drag the tips of u and v (snapped to the... Ages 15–16
2D + 3D Vectors in 3D space – sum, dot product, angle Mathematics · Vectors & Coordinate Geometry An Oxyz coordinate system rotates with the mouse or a finger, showing two vectors u and v with given coordinates.... Ages 17–18