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Two linear algebra questions - Vector geometry

  1. Nov 20, 2011 #1
    1. The problem statement, all variables and given/known data
    [URL]http://184.154.165.18/~devilthe/uploads/1321855187.png[/URL]


    2. Relevant equations
    No idea.


    3. The attempt at a solution
    Alright...so really no idea what to do here...never did any examples like this in class and have scoured over my notes for 2 hours now trying to figure this out...and can't lol.

    I tried finding the vector UV and then finding a vector that is orthogonal to that with no success...

    1. The problem statement, all variables and given/known data
    [URL]http://184.154.165.18/~devilthe/uploads/1321923155.png[/URL]


    2. Relevant equations
    Included?


    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    Again, not much clue on what to do here...actually no clue at all :(

    I know it sounds like I'm trying to freeload but I've already completed 7/9 of my other homework questions it's just these two that I have no idea how to do...
     
    Last edited by a moderator: Apr 26, 2017
  2. jcsd
  3. Nov 20, 2011 #2
    Have you guys covered cross products yet?
     
  4. Nov 20, 2011 #3
    No we have not...I saw that on another site as an answer to this question but had no idea how they got the answer.
     
  5. Nov 21, 2011 #4

    NascentOxygen

    User Avatar

    Staff: Mentor

    Let the vector you seek be [x1 y1 z1]
    As it is perpendicular to [3 -10 4], by calculating the dot product
    we can say 3.x1 -10.y1 + 4.z1 = 0
    ... and similarly for the second vector.

    We now have 2 equations in 3 unknowns.
    So let z1 be any convenient value, I chose z1 = 1.
    Solve for x1 and y1.

    Check that the resultant vector is perpendicular to both of the given vectors.
     
  6. Nov 21, 2011 #5
    Thanks Nascent, got it!
     
  7. Nov 21, 2011 #6

    NascentOxygen

    User Avatar

    Staff: Mentor

    Maybe then try it with z1=2, and comment on what you discover.
     
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