1 / 12

Algebraic Vectors & Parametric Equations: Concepts and Operations

Learn about the algebraic properties of vectors and how to write equations in parametric form. Understand vector operations and their applications in various graphs.

wendip
Download Presentation

Algebraic Vectors & Parametric Equations: Concepts and Operations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lesson 12 – 8 Algebraic Vectors & Parametric Equations Pre-calculus

  2. Learning Objective • To write equations of vectors and parametric equations

  3. In 12–7, we focused on the geometric aspect of vectors. 12–8 focuses on the algebraic properties Vectors & Parametric Equations (x, y) y x Note: the book will use ( , ) for a point AND a vector! Be careful! We will use for vectors is the norm/magnitude

  4. Unit Vector: vector with magnitude 1 (horizontal) Vectors & Parametric Equations (vertical) is the unit vector with the same direction as Component Form: Can be expressed as Polar Form:

  5. We can determine a vector if we know its initial and terminal points Vectors & Parametric Equations or 1. Given with initial point (2, 3) & terminal point (7, 9), determine the component form

  6. 2. Given with initial point (2, 3) & terminal point (7, 9), determine the polar form Vectors & Parametric Equations c 3. Given with initial point (2, 3) & terminal point (7, 9), determine the unit vector in the same direction as

  7. Vector operations: If and Vectors & Parametric Equations Vector sum: Vector difference: Scalar Multiplication: 4 and. Find such that

  8. In this picture, is a point and is a point. P(a, b) Vectors & Parametric Equations If you wanted to get to from , we could add a vector Q(x, y) Since we don’t know the size of the vector, we can multiply by a scalar to get to the point. Vector Equation of line: Now, The direction vector will be given to you, or you can find it by subtracting the 2nd point – 1st point that they give you.

  9. In this picture, is a point and is a point. P(a, b) Vectors & Parametric Equations Q(x, y) So, This leads to and These two equations are called parametric equations with parameter of the line

  10. 5. Determine a direction vector of the line containing the two points and . Then find the equation of the line & a pair of parametric equations of the line. Vectors & Parametric Equations Direction vector Vector Equation of line: Parametric Equations: and We can also represent other graphs (not just lines) in parametric.

  11. 6. Graph the curve with parametric equations and . Find an equation of the curve that contains no other variables but & . Vectors & Parametric Equations square put together 5 -3 3 Ellipse -5

  12. Assignment Pg. 651 #1, 3, 6, 9, 11, 15–18, 20, 21, 24, 29, 31, 33, 35

More Related