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Calculus: Vectors QUICK HELP PLEASE

  1. Sep 27, 2006 #1
    Calculus: Vectors QUICK HELP PLEASE!!!!

    Okay so i need a little help.

    Heres the problem.

    The question asks...

    Find a vector that has the same direction as <-2,4,2> but has length 6. :surprised

    So i Did the |v|= Sqrt( A1^2+A2^2+A3^2)= sqrt(24) which is how you begin to find the unit vector with the same direction. I get stumped on how to find it with length 6. The new vector with the same direction would be... <-2/Sqrt(24), 4/Sqrt(24), 2/Sqrt(24)... but.. what about the length of 6..?

    Can anybody help me? What do i do with this length of 6? :yuck:

    ... any help would be awesome!!!!!
     
  2. jcsd
  3. Sep 27, 2006 #2

    berkeman

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    Staff: Mentor

    Say you scaled the original vector by the same amount in all 3 dimensions. Which way would the scaled vector point?
     
  4. Sep 27, 2006 #3
    Do you just multiply everything by 6, or in your example by 3?
     
  5. Sep 27, 2006 #4

    radou

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    Homework Helper

    Hint: what is the manitude of the unit vector? :biggrin:
     
  6. Sep 27, 2006 #5
    The magnitude of the unit vector is sqrt(24) as i stated above. That is sqrt(24) of the original vector.
     
  7. Sep 27, 2006 #6
    ???? Help?
     
  8. Sep 27, 2006 #7
    No, it's one. That's why it is called " unit vector". So what do you have to do to get a vector of length 6 pointing in the same direction?
     
  9. Sep 27, 2006 #8
    Do u multiply or divide by 6? Im seriously lost as in how to get the new vector which i have found the direction too, to get a length of 6.. im totally lost. I would assume you multiply by 6, thus it would be length of 6?
     
  10. Sep 27, 2006 #9
    That's right. Think of it as an stick which is one cm long and pointing in some direction - to get a stick with a length of 6 cm and pointing in the same direction, you have to stick six of these sticks together.
     
  11. Sep 27, 2006 #10
    Okay so i need to multiply the new vector by 6. That means <a1*6, a2*6,a3*6>? Do u see what i mean?
     
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