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Find Vector C when given Vector A & B.

  1. Jan 13, 2014 #1
    This is from Schaum's 3000 solved Physics problems (1.75). The teacher attempted to guide us to solve it but me and a few classmates are still struggling to figure this out.

    1. The problem statement, all variables and given/known data
    Vector A = 3i + 5j - 2k
    Vector B = -3j + 6k
    Find a Vector C such that 2A + 7B + 4C = 0


    3. The attempt at a solution

    This looks a lot like Linear Algebra, something I am not particularly skilled in, however I think I gave it a decent shot.

    Ax = 3
    Ay = 5
    Az = -2

    Bx = -3
    Bz = 6

    2(3) + 7(-3) + 4(Cx) = 0
    Cx = 15/4 = 3.75

    2(5) + 0 + 4(Cy) = 0
    Cy = -10/4 = -5/2 = -2.5

    2(-2) + 7(6) + 4(Cz) = 0
    Cz = -38/4 = -19/2 = -9.5

    So therefor Vector C = (15/4)i - (5/2)j - (19/2)k

    The real solution is C = -1.5i + 2.75j - 9.5k

    Looks like I got Cz correct, but I can't figure out how to get Cx and Cy.
     
  2. jcsd
  3. Jan 13, 2014 #2

    jedishrfu

    Staff: Mentor

    First off your B components are wrong Bx=0 By=-3 and Bz=6

    and you have three equations to get the three C components:

    2Ax + 7Bx + 4Cx = 0

    2Ay + 7By + 4Cy = 0

    2Az + 7Bz + 4Cz = 0

    so its simple algebra from here
     
  4. Jan 13, 2014 #3

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Should be By=-3 not Bx ?

    Edit: jedishrfu beat me to it.
     
  5. Jan 13, 2014 #4
    Oh simple mistake ha. Thanks!
     
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