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Finding vectors and magnitude

  1. Jun 9, 2015 #1
    1. The problem statement, all variables and given/known data

    Find a vector in the direction opposite to <-4,1,2>, that has a magnitude of 3.

    2. Relevant equations
    I think that I did the first part of the problem correctly:
    <-4,1,2>
    magnitude= sqrt[ (-4)^2+1^2+2^2 ]
    = sqrt(16+1+4)
    = sqrt(21)
    (-4/sqrt(21), 1/sqrt(21), 2/sqrt(21) )
    to get the opposite direction, I would just change the signs
    (4/sqrt(21), -1/sqrt(21), -2/sqrt(21) )

    But I am confused at where to go from here. What does it mean "that has a magnitude of 3"? I may have approached this problem incorrectly. Any help would be great. Thank you for stopping by.
     
  2. jcsd
  3. Jun 9, 2015 #2

    Zondrina

    User Avatar
    Homework Helper

    You have found a normal vector. The magnitude of a normal vector is ##1##.

    Perhaps the answer is more trivial than it first appears, just think:

    $$\sqrt{a^2 + b^2 + c^2} = 3$$

    Select a vector ##<a, b, c>## such that the above is satisfied. Multiplying the original vector by ##-1## will help. In fact, one is the loneliest one, and the only one you'll ever need for this problem.
     
  4. Jun 9, 2015 #3
    As Zondrina has pointed out, you have correctly determined a unit vector in the desired direction. Now, what do you need to multiply this unit vector by to produce a vector having the same direction, but with a magnitude of 3?

    Chet
     
  5. Jun 9, 2015 #4
    Ah, okay. I think that I was making this problem more difficult than it actual is. Thank you so much for the help!
     
  6. Jun 10, 2015 #5

    Mark44

    Staff: Mentor

    Removed "Calc III" from thread title -- this is really a precalc type of problem. Also moved thread to the precalc forum section.
     
  7. Jun 23, 2015 #6
    How is this a pre-calc problem if I'm in calc 3 and this is the first time that I've dealt with this? Did my university just not cover this? Or am I behind?
     
  8. Jun 23, 2015 #7

    Mark44

    Staff: Mentor

    Vectors in R2 and R3 are often covered in precalculus with trig courses.
     
  9. Jun 23, 2015 #8

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    No limits, no derivatives, no integrals = no calculus.

    Your calc 3 course may simply be providing a refresher on basic vector math before jumping into vector calculus.
     
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