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Finding a unit vector orthogonal to

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a unit vector that is orthogonal to both i + j and i + k.

    I know I can solve this using the cross product of the two. But This chapter is about
    dot product and not cross product.

    I am not sure how I could go about solving this problem using the properties of a dot product.

    This is just a review, in test I would use the cross product.
     
  2. jcsd
  3. Sep 27, 2009 #2
    Thinking about this, I think I could use this formula :

    A*B = |A||B| cos(theta);

    =

    B / |B| = |A|cos(theta) / A

    Where A is the displacement vector from the given vector, and theta should be 90 deg.

    Thus I would find a unit vector, B, perpendicular to the displacement vector of the
    given vectors, which is parallel to Each of the 2 given vector.

    Is this assumption correct?
     
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