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Perpendicular 3D Vector Problem

  1. Feb 5, 2010 #1
    1. The problem statement, all variables and given/known data
    Give an example of a vector perpendicular to [6,2,3] that has the same length.

    2. Relevant equations
    Distance formula between two points on a 3D plane:
    Sqrt[(X1-X2)2 + (Y1-Y2)2 + (Z1-Z2)2]

    3. The attempt at a solution
    In 2D space, the perpendicular vector of [X,Y] is [-Y,X]. However, I know that 3D vectors have an infinite number of perpendicular vectors. Then I thought to myself that I should use the distance between to points to figure out the length, but since the problem does not give me the second point, I do not know what the length of the line is. I was thinking of starting at the origin, since the line from the origin to the point is the hypotenuse of the triangle the points make in 3D. I got 6.2, but now do not know how to go from here. Help is very appreciated.

    P.S. Just for further learning, how would I show that two vectors are perpendicular in the same equation?
  2. jcsd
  3. Feb 5, 2010 #2


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    Have you learnt about "scalar product" or "dot product" of two vectors?

  4. Feb 5, 2010 #3
    No, not yet. Only a sophmore in high school. If those concepts A) are on the SAT and B) help me find the answer, an explanation would be very appreciated.
  5. Feb 5, 2010 #4


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