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Math Help - IB Vectors: Find scalars

  1. #1
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    IB Vectors: Find scalars

    Two vectors are defined as a= (-3, 1, 4) and b= (6, -6, -5). Find values of the scalars X and Y if Xa+Yb is equal to:
    (-36, 32, 33).



    I would really like to attempt this problem myself. So, If anyone could please explain how to solve I would really appreciate it!
    Thanks in advance!!!
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  2. #2
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    Quote Originally Posted by overduex View Post
    Two vectors are defined as a= (-3, 1, 4) and b= (6, -6, -5). Find values of the scalars X and Y if Xa+Yb is equal to:
    (-36, 32, 33).



    I would really like to attempt this problem myself. So, If anyone could please explain how to solve I would really appreciate it!
    Thanks in advance!!!
    I've left enough gaps for you to lay some claim to the solution for yourself:

    On the one hand, X(-3, 1, 4) + Y(6, - 6, -5) = (-3X + 6Y, ...........)

    But on the other hand X(-3, 1, 4) + Y(6, - 6, -5) = (-36, 32, 33).

    Therefore:

    -3X + 6y = -36 .... (1)

    ..... (2)

    ....... (3)

    Equations (1), (2) and (3) are to be solved simultaneously for X and Y. Choose two of the equations and solve. Check that the resulting solutions satisfy the third equation (if they didn't, then there'd be no solution at all - all three equations have to be satisfied).
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