1 / 11

Vectors

Vectors. Objectives:. Find the magnitude of the vector Find component form Add and subtract vectors. A vector has both direction and magnitude . A vector begins with an initial point, usually P, to a terminal point, usually Q.

chun
Download Presentation

Vectors

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. Vectors

  2. Objectives: • Find the magnitude of the vector • Find component form • Add and subtract vectors

  3. A vector has both direction and magnitude. A vector begins with an initial point, usually P, to a terminal point, usually Q. A little reminder for terminal point: to terminate is to end, so the terminal point ends the line. Graph it as you would a ray. For example at right, the initial point is P(0, 0), and the terminal point is Q(-6, 3). Find the magnitude of a vector Q(-6, 3) P(0, 0)

  4. Write the following Component Form =‹x2 – x1, y2 – y1› or <u,v> <-6 – 0, 3 – 0> <-6, 3> is the component form. Next, use the distance formula to find the magnitude. |PQ| = √(-6 – 0)2 + (3 – 0)2 = √62 + 32 = √36 + 9 = √45 or 3√5 ≈ 6.7 Write the component form Q(-6, 3) P(0, 0)

  5. Initial point is P(0, 2). Terminal point is Q(5, 4). Graph the ray starting at P, and go through Q. See picture. Then start looking for component form and magnitude. Graph Vector

  6. Write the following Component Form =‹x2 – x1, y2 – y1› or <u,v> <5 – 0, 4 – 2> <5, 2> is the component form. Next use the distance formula to find the magnitude. |PQ| = √(5 – 0)2 + (4 – 2)2 = √52 + 22 = √25 + 4 = √29 ≈ 5.4 Write the component form

  7. Initial point is P(3, 4). Terminal point is Q(-2, -1). Graph the ray starting at P and going through Q. See picture. Then you can start looking for component form and magnitude. Graph Vector

  8. Write the following Component Form =‹x2 – x1, y2 – y1› or <u,v> <-2 – 3, -1 – 4> <-5, -5> is the component form. Next use the distance formula to find the magnitude. |PQ| = √-2 – 3)2 + (-1– 4)2 = √(-5)2 + (-5)2 = √25 + 25 = √50 or 5√2 ≈ 7.1 Write the component form

  9. Adding Vectors • Two vectors can be added to form a new vector. • To add u and v on a graph, place the initial point of v on the terminal point of u. • ♫ Take note! The sum of the vectors is a new vector from the initial point of u to the terminal point of v. • You can also add vectors algebraically. • You may put the initial point of u on the terminal point of v. This has lead to the name “the parallelogram rule”.

  10. What does this mean? • Adding vectors: Sum of two vectors The sum of u = <a1,b1> and v = <a2, b2> is u + v = <a1 + a2, b1 + b2> • In other words: add your x’s to get the coordinate of the first number in component form, and add your y’s to get the coordinate of the second number in component form.

  11. Example: • Let u = <3, 5> and v = <-6, 1> • To find the sum vectoru + v, add the x’s and add the y’s of u and v. u + v = <3 + (-6), 5 + (-1)> = <-3, 4> There are 6 of these on the test Wednesday!!! Adjusted by Kitchen

More Related