Combine Directed Displacements by Component
Adding vectors combines horizontal components and vertical components separately.
About 25 minutes, plus any extended practice
Open lesson 1Precalculus: Vectors and Parametric Lines
Vectors represent directed quantities through components, while parametric equations describe coordinates using a shared parameter. Component arithmetic, magnitude and dot product answer different questions and therefore produce different kinds of results.
Before you begin
- Add signed coordinates; evaluate square roots; substitute one expression into another.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Compute a Nonnegative Vector Length
A vector’s component displacements form perpendicular legs of a right triangle.
About 25 minutes, plus any extended practice
Open lesson 2Distinguish a Dot Product from a Vector Sum
A dot product multiplies corresponding components and sums the products.
About 25 minutes, plus any extended practice
Open lesson 3Replace a Shared Parameter with an Input Expression
A parametric line defines x and y using the same parameter.
About 25 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- OpenStax mathematical topic reference: topic reference — Precalculus: Vectors and Parametric Lines
These references informed the topic selection. They do not certify complete standards alignment.