1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Algebraic vectors

  1. Jun 4, 2006 #1
    if i had to find a vector of magnitude 27 units which is parallel to 3i+ 4j, what do i have to do first? would i express my answer in ordered pair notation?
     
  2. jcsd
  3. Jun 4, 2006 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I would express your answer in terms of unit vectors. Ordered pair notation is uaually used to define co-ordinates. Remember parallel vectors must be multipuls of each other.

    ~H
     
  4. Jun 4, 2006 #3
    would this be a sufficient answer:

    let u be the vector.

    the magnitude of 3i + 4j is 5

    27/5 = 5.4

    since parallel vectors are multiples of each other, we can just multiply (3i + 4j) by the scalar 5.4

    so u = 5.4(3i + 4j)
    = 16.2i + 21.6j

    this is what i came up with before but it seems messy (decimals) and and kind of an inefficient solution
     
  5. Jun 4, 2006 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Seems good to me, but why not write your answer as:
    [tex]u=\frac{27}{5}(3i+4j)[/tex]

    Note that [itex]\frac{1}{5}(3i+4j)[/itex] is a UNIT vector.
     
  6. Jun 4, 2006 #5
    looks much better. thanks!
     
  7. Jun 4, 2006 #6

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Who said it wasn't a unit vector?
     
  8. Jun 4, 2006 #7

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Noone. I just wanted to emphasize that, so that OP could see how a unit vector naturally would occur in his expression.
     
  9. Jun 4, 2006 #8

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Ahh right, I thought I'd made a mistake somewhere :confused: .
     
  10. Jun 4, 2006 #9

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    No, but I wanted OP to see why your suggestion
    is, indeed, the most natural one.
     
  11. Jun 4, 2006 #10

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Good point, I should have emphisised (but I didn't get the chance :wink: )
     
  12. Jun 4, 2006 #11
    guys, i have some more questions if you don't mind.

    state whether the following expressions are vectors, scalars or meaningless:
    a) (a+b) • (a+c)
    b) (a • a)b
    c) (a • b)• c(b × c)

    note that all the letters are vectors (so picture arrows on top of them)

    mostly i need to clairify some things. first, whats the difference between a scalar and something meaningless? also for b) and c), what does something like (a • a)b compute to. does the b multiply, or dot, or cross or what?
     
  13. Jun 4, 2006 #12

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Something "meaningless" is an indicated operation between quantities that the operation in question cannot, by definition, be used upon.
     
  14. Jun 4, 2006 #13
    oh ok, so since the dot and cross products are only applicable to vectors, if a scalar was involved in one of them, the result would be meaningless?

    to restate my other question, what does the b part of (a • a)b compute to. does the b multiply, or dot, or cross or what?
     
  15. Jun 4, 2006 #14

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Remember that you have 3 basic product operations with vectors:
    1. Dot product: Takes two vectors and produces a scalar.
    2. Cross product: Takes two vectors and produces a vector.
    3. Scalar multiplication: Takes a scalar and a vector, produces a vector that is parallell to the original vector.
     
  16. Jun 4, 2006 #15
    thanks for the summary but the way (a • a)b is written, and considering b is a vector and not a scalar, what is the operation here?
     
  17. Jun 4, 2006 #16

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    What does a parenthesis usually signify for the order of operations performed?
     
  18. Jun 4, 2006 #17
    so i think your referring to doing the inside of the brackets first; a dot product operation yielding a scalar. so then does it leave a scalar multiplying a vector?
     
  19. Jun 4, 2006 #18

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    What do YOU think?
     
  20. Jun 4, 2006 #19
    lol that's what i think, i do have some doubt however because as you look at c) (a • b) • c(b × c), the second part of the question (c(b × c)) is somewhat confusing. you basically get a vector multiplying a vector without dot or cross product operation (the only two ways you can muliply vectors i'm aware of). although this does not change the outcome of the question since the first part of the question is a scalar and yielding the result meaningless.
     
  21. Jun 4, 2006 #20

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Correct!
    Either way you are looking upon the last one, either as:
    [tex]((a\cdot{b})\cdot{c})(b\times{c})[/tex]
    or as:
    [tex](a\cdot{b})\cdot({c}(b\times{c}))[/tex]
    the expressions are meaningless.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Algebraic vectors
  1. Vector algebra (Replies: 4)

Loading...