Equivalent Vectors...3

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Jan 22, 2022.

  1. nycmathguy

    nycmathguy

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    Section 6.3

    Screenshot_20220121-190827_Samsung Notes.jpg

    IMG_20220122_124937.jpg

    IMG_20220122_124955.jpg
     
    nycmathguy, Jan 22, 2022
    #1
  2. nycmathguy

    MathLover1

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    correct
     
    MathLover1, Jan 22, 2022
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    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    I feel like traveling on into math land.
     
    nycmathguy, Jan 22, 2022
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  4. nycmathguy

    Country Boy

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    NO! It is not correct! You are comparing the lengths of the vectors but having the same length is not enough. For example, the vector from (0, 0) to (4, 0) and the vector from (0, 0) to (0, 4) have the same length but are NOT "equivalent" because they do not have the same direction.

    One way to show that two vectors are equivalent is to show that they have the same length and the same direction.
    For example, in problem 18, u has initial point (8, 1) and terminal point (13, -1). It has lenght $\sqrt{(8- 13)^2+ (1- (-1))^2}= \sqrt{5^2+ 2^2}= \sqrt{29}$ as you say. It also has direction arctan(2/5) degrees. v has initial point (-2, 4) and terminal point (-7, 6). Its length is $\sqrt{(-2- (-7))^2+ (4- 2)^2}= \sqrt{5^2+ 2^2}=\sqrt{29}$ as before. The two vectors are the same length but are they in the same direction? The direction of v is arctan(2/5) as before so yes, they are in the same direction, so are equivalent vectors, but your reasoning is incorrect because you did not check the directions.
     
    Country Boy, Jan 23, 2022
    #4
  5. nycmathguy

    nycmathguy

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    Are you saying that MathLover1 is wrong? She's pretty good at solving math problems.
     
    nycmathguy, Jan 23, 2022
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