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Math Help - Orthogonal /parallel or neither

  1. #1
    Faz
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    Orthogonal /parallel or neither

    a)Determine whether the lines (x-1)/4=(y+1)/2=(z-3)/-1 and
    (x-1)/1=(y+1)/2=(z-3)/8 are orthogonal , parallel or neither.


    b)Determine whether the following lines (x-3)/3 = (y+1)/-2 = (z-3)/5 contains the point (6,-3,8)

    c)Find equation of the line containing the given point (5,3,4) and parallel to the vector
    -> -> ->
    2 i + 5 j - 8 K

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  2. #2
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    Hello, Faz!

    These are very basic questions.
    . . Exactly where is your difficulty?


    a) Determine whether the lines: . \frac{x-1}{4}=\:\:\frac{y+1}{2} \:=\:\frac{z-3}{-1}\;\text{ and }\;\frac{x-1}{1}=\:\:\frac{y+1}{2}\:=\:\frac{z-3}{8}
    are orthogonal, parallel or neither.
    The direction vectors of the lines are: . \vec u \:=\:\langle 4,2,-1\rangle\:\text{ and }\:\vec v \:=\:\langle 1,2,8\rangle


    Since \vec u is not a scalar multiple of \vec v, they are not parallel.


    We find that: . \vec u \cdot \vec v \:=\:\langle 4,2,\text{-}1\rangle\cdot\langle1,2,8\rangle \:=\:(4)(1)(+(2)(2) + (\text{-}1)(8) \:=\:0

    Therefore: . \vec u \:\perp \;\vec v




    b) Determine whether the line . \frac{x-3}{3}\:=\:\frac{y+1}{-2} \:=\:\frac{z-3}{5} .contains the point (6,-3,8)
    Do the coordinates satisfy the equation? . . . Plug them in!



    c) Find an equation of the line containing the given point (5,3,4)
    and parallel to the vector: . 2\vec i + 5\vec j - 8\vec k
    We have a point P(5,3,4) and the direction vector \vec v \:=\:\langle 2,5,\text{-}8\rangle

    . . . Well?

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