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Math Help - Finding coordinates given vector eqns and point

  1. #1
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    Finding coordinates given vector eqns and point

    How do I do this,

    Point A(3,0,-2) lies on the line r=3i-2k+ t(2i-2j+k) where t is a real parameter. FInd the coordinates of one point which is 6 units from A, and on the line.

    I put the equation of the line to parametric form and then, subtracted A from these parametric equations.. but I dont know what I am doing really.

    THank you so much!
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  2. #2
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    Re: Finding coordinates given vector eqns and point

    Hey Tutu.

    Hint: Try getting your line in terms of L(t) = a + n*t where n is a unit vector with length 1 and a is your starting point you are starting from and note that for some value t, it will be exactly t units in the direction of n from a.
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  3. #3
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    Re: Finding coordinates given vector eqns and point

    Thanks but isn't it already in terms of a+N*t with r=3i-2k + t(2i-2j+k)?
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  4. #4
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    Re: Finding coordinates given vector eqns and point

    Quote Originally Posted by Tutu View Post
    Point A(3,0,-2) lies on the line r=3i-2k+ t(2i-2j+k) where t is a real parameter. FInd the coordinates of one point which is 6 units from A, and on the line.

    If A: (3,0,-2)~\&~D: <2,-2,1> then let U=\frac{D}{\|D\|}.

    Define \ell(t)=A+t\cdot U. Then your answer is \ell(\pm6) WHY?
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