Simple Vector Problem

  1. 1. The problem statement, all variables and given/known data

    Find two vectors, v1, and v2, whose sum is <-4,1,1>, where v1 is parallel to <2,5,-4>, and where v2 is perpendicular to <2,5,-4>



    2. Relevant equations

    I am guessing I use the cross product for this equation, but I'm confused about how to start this problem.

    3. The attempt at a solution

    any hlep at all would be greatly appreciated!
     
  2. jcsd
  3. Mark44

    Staff: Mentor

    Don't use the cross product.

    Write v1 and v2 using coordinates. You're given that they add to <-4, 1, 1>. You're also given that v1 is parallel to <2, 5, -4>, which means that v1 is some constant multiple of <2, 5, -4>. You're also given that v2 is perpendicular to <2, 5, -4>. Two vectors being perpendicular should suggest a particular operation.
     
  4. So, first I realized that v1= K<2,5,-4>

    Then I figured that since v1+v2=sum, ;
    then:

    <4,1,1> - K<2,5,-4> = v2

    Now, what process would I use to find K?
     
  5. Mark44

    Staff: Mentor

    Then what are the coordinates of v1?

    How about finding coordinates for v2 first?

    Also what can you do with the given information that v2 is perpendicular to <2, 5, -4>?
     
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