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Math Help - vectors and points in skew lines given parametric equations

  1. #1
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    vectors and points in skew lines given parametric equations

    Having trouble converting parametric equations to skew line equations!

    line 1- x=1+2r, y=1+2r, z= -3+r

    line 2- x=-2, y=s, z =2+s

    a.) Show that these lines are perpendicular to vector v=
    [1
    -2
    2]
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  2. #2
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    Re: vectors and points in skew lines given parametric equations

    Quote Originally Posted by jnow2 View Post
    line 1- x=1+2r, y=1+2r, z= -3+r
    line 2- x=-2, y=s, z =2+s
    a.) Show that these lines are perpendicular to vector v=
    [1
    -2
    2]
    Show the vectors <2,2,1>~\&~<0,1,1> perpendicular to the given vector <1,-2,2>.
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  3. #3
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    Re: vectors and points in skew lines given parametric equations

    Thankyou! but cross product for the vector of line 2 keeps equaling 4 and not 0?
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  4. #4
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    Re: vectors and points in skew lines given parametric equations

    Quote Originally Posted by jnow2 View Post
    Thankyou! but cross product for the vector of line 2 keeps equaling 4 and not 0?
    It is dot product, not cross product.
    <2,2,1>\cdot<1,-2,2>=2(1)+(2)(-2)+(1)(2)=0
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  5. #5
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    Re: vectors and points in skew lines given parametric equations

    Cross product? You mean dot product, don't you? <0, 1, 1>\cdot<1, -2, 2>= 0(1)+ 1(-2)+ 1(2)= -2+ 2= 0
    You must have dropped the "-" from -2.
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