Mathematics — first biennium · Lesson
Multiplying a vector by a scalar means multiplying both components. A linear combination such as 2u−v is built component by component using the same coefficients.
Prerequisites: Vectors in the plane
Goal: Multiply vectors by scalars and build linear combinations component by component.
In this lesson: Multiply vectors by scalars and build linear combinations component by component.
New concept: Multiplying a vector by a scalar λ means multiplying both components by λ. A linear combination αu+βv is therefore built by scaling the vectors and adding corresponding components.
How to proceed: Write 2u first, then subtract v coordinate by coordinate. The minus sign in front of v changes both of its components.
You can already assume: Vectors in the plane.
The three arrows show u, v and the combination w=2u−v in the same Cartesian plane.
Completed exercises: 0/5 · Correct on first attempt: 0
Write 2u first, then subtract v coordinate by coordinate. The minus sign in front of v changes both of its components.
Data / situation: u=(2,-3), v=(-1,-4). Calculate w=2u-v.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.