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Cakculating vectors

  1. Sep 14, 2004 #1
    Please Help! I just don’t get it and I’ve been studying for hours.

    Question :
    Knowing that Vectors C = (4x-1y-3z) meters and D=(2x-3y-5x) meters
    Determine
    a. S=C-D
    b. │S
    c. The Unitary vector in the direction of S

    My Prof has given us a test one week after the first class and I just don’t get these study questions. I can add and multiply vectots but this stuff I just don’t get and there is noone to help.

    If anyone out there can help you’ll really be appreciated

    Pamela
     
    Last edited: Sep 14, 2004
  2. jcsd
  3. Sep 14, 2004 #2
    I don't get your notation. What are the base-vectors describing the directions ???

    Something like 6e_x + 7e_y. The e_x and e_y denote the x and y direction and these are the base-vectors. 6 and 7 are the components so this vector may also be written as (6,7).

    When adding or substracting just add or substract all components per direction. So for example (7,8) - (1,1) yields (6,7) or 6e_x + 7e_y

    Multiplying means multiply the components per direction and add up the outcomes: so this means (7,8)*(1,2) = 7*1 + 8*2 = 7+16=23

    If you take the squareroot of this you get the length of a vector = sqrt(23) like your question b.

    But first of all you need to know the components per direction. What are these j and m???
    Are you sure you got the notation right??? Just wondering


    regards
    marlon
     
  4. Sep 14, 2004 #3
    Changes

    Thanks Marlon I made the changes by editing my post. Maybe now my question is easier to understant

    Pamela
     
  5. Sep 14, 2004 #4
    So you have (4,-1,-3) and (-3,-3,0)

    I think you are able to continue right now. Just do what a answered in the first post

    marlon
     
  6. Sep 14, 2004 #5
    for example a would be (7,2,-3) or S =7x + 2y - 3z

    regards
    marlon
     
  7. Sep 14, 2004 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    It is more common to use i, j, and k where you are using x, y, z but I think I understand what you mean:

    C = (4x-1y-3z) is what I would call 4i-1j-3k or, more simply just <4, -1, -3> where the basis vectors are understood to be in the x, y, z, directions.

    So, C= <4, -1, -3> and D= <2, -3, -5>. Surely your text bood mentions early that vectors written in "component" form can be added and subtracted just by working with each "component" separately. S= C- D is simply <4- 2, -1-(-3),-3-(-5)> =
    <2, 2, 2>.

    The length of a vector comes from the Pythagorean theorem: [itex]\sqrt{2^2+ 2^2+ 2^2}= \sqrt{12}= 2\sqrt{3}[/itex].

    A "unitary" vector (I would say "unit" vector) in a given direction is a vector of length 1 in that direction. In particular, for any vector S, to find a unit vector in the same direction, just divide S by its length: S/|S| which is, again, done component by component. In this problem, since S= <2, 2, 2> and |S|= [itex]2\sqrt{3}[/itex], The unit vector in the direction of S would be [itex] \frac{<2, 2, 2>}{2\sqrt{3}}[/itex].
    That is, of course, [itex]\{\frac{1}{\sqrt{3},\frac{1}{\sqrt{3},\frac{1}{\sqrt{3}>[/itex]. It is in the same direction as S simply because it has all components the same and its length is [itex]\sqrt{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}= 1[/itex].
     
  8. Sep 14, 2004 #7
    Isn't the second vector 2x-3y-5x??? Or is it 2x-3y-5z. In that case my previous answer is not true. Then you would have (4,-1,-3) - (2,-3,-5)=(2,2,2)

    marlon
     
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