Vectors help to solve problems

Vectors allow us to represent points, directions, and movements in the plane using coordinates. By using vector addition, subtraction, and scalar multiplication, we can solve geometric problems more systematically.

Important properties

• Vectors can represent the position of points relative to an origin.

• Adding vectors corresponds to moving along one vector and then another.

• The difference between two position vectors gives the vector from one point to another.

• Vectors can be used to prove collinearity, parallelism, and to calculate midpoints and ratios.