← Math: Vectors and Coordinates

⇄ Sync
Length

Program
History and progress transfer
Choose a topic — problems will keep coming one after another for as long as you like

Theory of all steps of the program by blocks. Open a topic to read it.

How a session goes

A session is 10–90 minutes: a warm-up on what you've learned, new steps with short theory and problems, practice. Each problem gives two tries: 100 points on the first, 60 on the second; after the second mistake the correct answer is shown. You move on in the program if 70 % of the problems are solved.

Problems with numbers are generated anew every time a step is repeated. A fractional answer can be entered with a comma, a point or as a fraction: 0,5, 0.5, 1/2. In Practice any topic is available without a timer.

About the course

Vectors and coordinates, length, addition and scalar multiplication, a basis, the dot product, angle and projection, the equation of a line and the distance from a point to a line, the circle, coordinates in space, the cross product and area, the equation of a plane. Grade 7–8 math plus sine and cosine is enough.

Course program: 27 lessons

Vectors and coordinates

  1. A vector and its coordinates
  2. Vector length and distance
  3. Addition and scalar multiplication
  4. Vector operations: more
  5. Expansion in a basis
  6. Checkpoint: vectors and coordinates

Dot product

  1. Dot product
  2. Angle between vectors
  3. Perpendicularity
  4. Vector projection
  5. Dot product: more
  6. Checkpoint: dot product

Lines in the plane

  1. Equation of a line
  2. A line through two points
  3. Parallel and perpendicular lines
  4. Distance from a point to a line
  5. Lines: more
  6. Checkpoint: lines in the plane

The circle

  1. Equation of a circle
  2. The circle: more
  3. Checkpoint: the circle

Vectors in space

  1. Coordinates in space
  2. Space: more
  3. Cross product
  4. Area via vectors
  5. The equation of the plane
  6. Checkpoint: vectors in space