1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Find a unit vector

  1. Oct 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Two vectors are given by the relations

    a = 2i-3j-3k
    b = 6i+2j+k

    Find unit vectors corresponding to a 3- dimensional orthogonal right handed coordinate system where one of the axes is parallel to [itex]_{}a[/itex] and another of the axes is perpendicular to [itex]_{}b[/itex]

    2. Relevant equations

    Cross rule: AXB = C
    3. The attempt at a solution

    I know from cross product that if we have two vectors in a plane then their multiple vector will also be perpendicular to them. So my vector AXB is : 3i-20j+22k ( perpendicular to a and b )

    Now I know they want unit vector which is : v/ magnitude of v but in the above case I was told to find the vector : Ax(AXB)...
    I am confused about this point. Can anyone clarify for me. Thanks
  2. jcsd
  3. Oct 7, 2011 #2


    User Avatar
    Science Advisor

    You are given a and b and asked to find "one unit vector that is parallel to a"- that should be easy- and another that perpendicular to b. As you say, axb is perpendicular to both a and b and so to b. You are then asked to find a third vector, c, say, that is perpendicular to both a and the new vector you just calculated. Yes, that is ax(axb). There is no problem with that- just do it! First find v= axb, then use that to find c= axv. I recommend first finding the vectors v and c and then dividing a, v, and c by their lengths to get unit vectors.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook