Combining Vectors

Reaching any point with two arrows

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A linear combination a·u + b·v stretches and adds vectors.
• Two non-parallel vectors reach every point of the plane, uniquely: a basis.
• Parallel vectors (zero determinant) only reach a line.

Steps

1. Stretch and add
2. Compute one
3. Hit the target
4. When it fails
5. Make them parallel
6. New coordinates