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How do I prove that A^B is orthogonal to A?

  1. Nov 9, 2011 #1
    1. The problem statement, all variables and given/known data

    If A = (2,-2,1) and B = (2, 0, -1)
    show by explicit calculation that

    i) A^B is orthogonal to A

    ii) (A^B)^B lies in the same plane as A and B by expressing it as a linear combination of A and B

    2. Relevant equations

    A^B = |A||B|sin θ

    3. The attempt at a solution

    I know that when you do the cross product of two vectors the result will be a vector that is perpendicular to both and I can draw a diagram to demonstrate. However I can't show it by explicit calculation. :(

    I thought maybe if I could prove that the angle between them was ∏/2...
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 9, 2011 #2
    If you know how to calculate cross product ^ , you will do A^B and if you find correctrly the value ~(itwill be a vector the result ,lets call it C) then you take the dot product of C with A and if it is zero they are orthogonal.

    since cos90 =0 and (A) dot (B)= A B cosθ

    ii)i think you can use the identity : a x ( b x c ) = b(ac) -c(ab) , b=a here
     
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