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Vectors Multiplication

  1. Oct 23, 2011 #1
    Actually I have two questions

    1. The problem statement, all variables and given/known data

    Vectors A and B are shown on the figure below. Which one of the
    following statements is correct?
    a) A . B = 0 and A × B ≠ 0
    b) A . B ≠ 0 and A × B = 0
    c) A . B ≠ 0 and A × B ≠ 0
    d) A . B = 0 and A × B = 0
    Picture: http://i.imgur.com/X0GB9.png

    2. Relevant equations

    A.B = AxBx + AyBy

    3. The attempt at a solution

    Obviously, the answer is zero. but the problem is the difference between A . B and A x B. I have long thought that those two are the same, but this question confused me.
    I tried google for a bit and found out that [ dot product (u . v) gives a scalar ] and [ cross product (u x v) gives a pseudovector ]. It's my first time hearing about a pseudovector =_=

    My second question is also about Vectors Multiplication

    1. The problem statement, all variables and given/known data

    A and B are the two vectors shown in the figure. Vector A is along the positive x
    axis and has a magnitude of 5 cm, and the vector B is in the x-y plane at an angle 30º
    with the positive x axis and has a magnitude of 4 cm. A × B =

    a) 20 cm2 in the +x direction b) 10 cm2 in the +y direction
    c) 10 cm2 in the +z direction d) 20 cm2 in the -y direction


    2. Relevant equations

    A.B = AxBx + AyBy

    3. The attempt at a solution

    When I tried to solve it I got C= 17.5 + 0, so the answer might be a.

    This cm^2 and the +z confused me, so I just wanted to confirm.
     
  2. jcsd
  3. Oct 23, 2011 #2
    Here is a re-fresher on dot and cross product.
    http://ltcconline.net/greenl/courses/107/vectors/dotcros.htm

    For 2 vectors A and B orthoganol ( at right angles) then the dot product A . B = 0, (ie there is no component of A is the same direction as B ( or visa-versa ) sometimes called the projection of A on B.

    But, the other part of the answer is A x B = 0 or A x B ≠ 0.

    What is your relevant equation for A x B??

    Well, you are multiplying a value in A with dimensions cm by one in B of dimension cm, so that would be cm^2.

    Axis x and y make a plane,
    Add another axis called z and you can work with volumes.
    The axis can also be labelled by the unit vectors i,j,k, which you might not have seen yet.
     
  4. Oct 24, 2011 #3

    Thank you for you reply,
    Yeah, I understood the first one thanks to the website you posted.

    first question answer: a) A . B = 0 and A × B ≠ 0
    and the answer for the second one is ' C= 17.5 + 0 '

    Thanks (*
     
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