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    western50's Avatar
    western50 Posts: 105, Reputation: 1
    Junior Member
     
    #1

    Jul 16, 2011, 10:25 PM
    cross product
    I am not sure how I should explain the following problems:

    If you take any two perpendicular unit vectors X and Y, then

    1. X\[Cross]Y is perpendicular to both X and Y

    2. X\[Cross]Y is also a unit vector

    3. If X and Y are unit vectors, but X is not perpendicular to Y, then can X\[Cross]Y be a unit vector? Why not?
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
    Expert
     
    #2

    Jul 18, 2011, 08:55 AM

    Recall that the definition of the cross product is:



    where is the smaller angle between and , and is a unit vector perpendicular to the plane containing and . If the magnitude of and are both 1, and is something other than 90 degrees, can the magnitude of the cross product ever be equal to 1?

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