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Homework Help: Vector components proof

  1. Oct 3, 2012 #1
    1. The problem statement, all variables and given/known data

    A is a vector

    Show that: a1 = x hat (dot) A
    a2 = y hat (dot) A
    a3 = z hat (dot)A

    2. Relevant equations

    A= (a1*x hat) + a2*y hat) + (a3* z hat)

    3. The attempt at a solution

    my hint says to take the dot product of both sides of the equation in (2) with each of the basis vectors in turn.

    Doing this I get A^2 = [(a1*x hat) + a2*y hat) + (a3* z hat)] dot A

    I dont know what to do next, or if thats even right.
  2. jcsd
  3. Oct 3, 2012 #2


    Staff: Mentor

    You haven't told us what a1, a2, and a3 are, nor have you said what "x hat" and the other two hats represent.

    Don't make us try to read your mind...
    Is this given? If so, you need to say so.

    A2 has no meaning - you can't just multiply a vector by itself. You can dot it with itself, but you don't get A2.
  4. Oct 3, 2012 #3


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    Science Advisor
    Homework Helper
    Gold Member

    Are ##\hat x, \hat y, \hat z## the unit vectors in the x,y, and z directions, more commonly known as i, j, and k? And is ##\vec A = a\mathbf{i} +b\mathbf{j} + c\mathbf{k}##? If so, the problem is pretty easy. Remember the basis vectors are perpendicular. What happens if you dot i into both sides?
  5. Oct 4, 2012 #4
    I tried what I thought you meant to try, here's what I did. I dotted both sides of the equation by x-hat in my case instead of ur i-hat example. Here's what I got. Dunno if on right track or not.

    [PLAIN]http://postimage.org/image/6zbkosjsp/ [Broken][/PLAIN]
    Last edited by a moderator: May 6, 2017
  6. Oct 4, 2012 #5
    What do you think [itex]\hat x \cdot \hat x[/itex] is?
  7. Oct 4, 2012 #6
    x hat dot x hat = x^2
  8. Oct 4, 2012 #7
    Mm, nope. What is the significance of the hat? What does a hat tell us about a vector?
  9. Oct 4, 2012 #8
    that it's a unit vector , which equals one?

    so x-hat (dot) x-hat = 1?
  10. Oct 4, 2012 #9
    That it's a unit vector, so its length is 1. Dot product of a vector with itself gives the length squared, but [itex]1^2 = 1[/itex], so yeah.
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