Vectors in space: sum, scaling, collinear and coplanar
Add vectors with the parallelepiped rule and in coordinates, multiply a vector by a number, and find out when three vectors lie in one plane.
- France: grade 12
- Germany: grade 12
- Palestine: grade 11
- Ukraine: grade 10
- Russia: grade 11
Guide
This follows Ukrainian Grade 10 geometry §40–41 in space. Vectors are a⃗ or AB⃗, coordinates are written a⃗(1; 2; 3).
The solid is the box ABCDA₁B₁C₁D₁; every vector starts at A. Turn the picture to see which vectors lie in one plane.
Common slips: adding lengths instead of vectors, multiplying coordinates instead of adding, and thinking any three vectors from one point are coplanar.