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Question concerning vectors

  1. Jan 31, 2009 #1
    I have this question in my book:-

    find the angle between the two vectors:
    A= i - 2j + 3k
    B= 2i + 3j -2k

    the solution is based on the scalar product rule.. (so the question is solved)...

    I`m just tryin to find another way to solve the problem? because I`m not really confident of vectors..

    I have a questions also:-
    Find the vector product of the two vectors:
    A= i - 2j + 3k
    B= 2i + 3j -2k
    now the answer is: -5i+8j+7k..

    now how could that resultant vector be perperndicular on A and B? it seems to have a "not right" angle (not 90 degree angle)..
    because if the origion is 0,0,0.. then -5i +8j+7k makes a "non right" angle (it would only be right if the answer was 0,0,xk where x is any number)

    if I`m mistaken about the origion being 0,0,0 then what is it?


    by the way, I`ve asked this question on "Y! asnwers", but none answered, so I`m posting here..
     
  2. jcsd
  3. Jan 31, 2009 #2

    CompuChip

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    Science Advisor
    Homework Helper

    If it makes you feel any better, you can draw them on a sheet of paper and use some geometry to find the angle... in the end you will end up using the exact same expression as you would using the inner product.

    First of all, (0, 0, xk) either does not make sense (when k is again a unit vector) or is confusing notation at the very best. I assume you meant x k = (0, 0, x).
    Why do you think it should be along the z-axis? It would make a right angle with any vectors in the (x, y) plane. If you take for example A = i + j, B = 3i - 2j, you will see that the vector product A x B gives something pointing in the k-direction only. The vectors you gave have components along all three axes though. If you draw them on a piece of paper you will see that (A x B) is perpendicular to A (makes a right angle with A), as well as with B.
     
  4. Jan 31, 2009 #3
    I got it, thank you,

    "It would make a right angle with any vectors in the (x, y) plane. If you take for example A = i + j, B = 3i - 2j, you will see that the vector product A x B gives something pointing in the k-direction only."

    Actually that was the problem, I was thinking of the first two vectors as being only on the x,y plane.

    Thanx
     
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