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Math Help - I am looking for help with the following

  1. #1
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    I am looking for help with the following

    The book states

    Three Vectors

    U= Uxi + 3j+2k
    V= -3i + Vyj+3k
    W= -2i + 4j+Wzk

    are mutally perpendicular Use dot product to solve for the componets
    Ux,Vy & Wz

    I do not know how to begin and am pretty confused the answer are

    Ux=2.875
    Vj= .857
    Wz=-3.143

    Can anyone help??
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jaycas21
    The book states

    Three Vectors

    U= Uxi + 3j+2k
    V= -3i + Vyj+3k
    W= -2i + 4j+Wzk

    are mutally perpendicular Use dot product to solve for the componets
    Ux,Vy & Wz

    I do not know how to begin and am pretty confused the answer are

    Ux=2.875
    Vj= .857
    Wz=-3.143

    Can anyone help??
    You have three unknowns Ux, Vy and Wz. You are told that they are
    mutually perpendicular, and you are to use the dot product.

    The dot product of perpendicular vectors is zero, so you have:

    U.V=0,
    U.W=0,
    V.W=0.

    Form these dot products and you will have three linear simultaneous
    equations which you then need to solve.

    Dot product of two vectors: x_1i+x_2j+x_3k and y_1i+y_2j+y_3k is:

    x_1y_1+x_2y_2+x_3y_3,

    where i, j and k are the unit vectors along a set of perpendicular axes.

    RonL
    Last edited by CaptainBlack; January 29th 2006 at 02:55 AM. Reason: error in the explanation of dot product
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  3. #3
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    I am still not getting the answers in the book
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  4. #4
    MHF Contributor
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    Quote Originally Posted by jaycas21
    The book states

    Three Vectors

    U= Uxi + 3j+2k
    V= -3i + Vyj+3k
    W= -2i + 4j+Wzk

    are mutally perpendicular Use dot product to solve for the componets
    Ux,Vy & Wz

    I do not know how to begin and am pretty confused the answer are

    Ux=2.875
    Vj= .857
    Wz=-3.143

    Can anyone help??
    If two vectors are perpendicular, then their dot product is zero.

    Since the 3 given vectors are mutually perpendicular, then,
    U dot V = 0
    U dot W = 0
    V dot W = 0

    U dot V = (Ux)(-3) +3(Vy) +2(3) = 0
    -3Ux +3Vy +6 = 0
    -Ux +Vy +2 = 0 --------------(1)

    U dot W = (Ux)(-2) +3(4) +2(Wz) = 0
    -2Ux +12 +2Wz = 0
    -Ux +6 +Wz = 0 -------------(2)

    V dot W = -3(-2) +(Vy)(4) +3(Wz) = 0
    6 +4Vy +3Wz = 0 --------(3)

    3 equations, 3 unknowns, solvable.

    (2) minus (1),
    6 +Wz -Vy -2 = 0
    Wz = Vy -6 +2
    Wz = Vy -4 --------------(i)

    Substitute that into (3),
    6 +4Vy +3(Vy -4) = 0
    6 +4Vy +3Vy -12 = 0
    7Vy -6 = 0
    7Vy = 6
    Vy = 6/7 = 0.857 ----------answer.

    Substitute that into (i),
    Wz = 0.857 -4 = -3.143 ---------answer.

    Substitute the 0.857 for Vy into (1),
    -Ux +Vy +2 = 0 -----(1)
    -Ux +0.857 +2 = 0
    -Ux +2.857 = 0
    Ux = 2.857 --------------answer.

    ------------------------
    Zeez, late again.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by jaycas21
    The book states
    U= Uxi + 3j+2k
    V= -3i + Vyj+3k
    W= -2i + 4j+Wzk

    Ux=2.875
    Vj= .857
    Wz=-3.143

    Can anyone help??
    U.V=-3Ux+3Vy+6=0 .......equation1
    U.W=-2Ux+12+2Wz=0 ....equation2
    V.W=6+4Vy+3Wz=0 .......equation3

    This system has the solution that your book gives (as can be checked
    by substituting its values into the equations.

    RonL
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