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Math Help - Two Vector Problems

  1. #1
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    Two Vector Problems


    1. The problem statement, all variables and given/known data

    Find the implicit form for the plane that contains the origin and the line:

    L(t) = <1+t,1-t,2t>



    3. The attempt at a solution'

    So, the point P = (1,1,0) and vector v= <1,-1,2>.

    For this problem, I am guessing I need to find a normal vector and use the point (1,1,0) to find the implicit equation, but how am I supposed to find another vector other than <1,-1,2> to get the normal vector?

    __________________________________________________ __________________________________________________ ______________


    #2. The function f(t) = (t^@,1/t) represents a curve in the plane parametrically. write an equation in parametric form for the tangent line to this curve at the point where t= 2.

    So I solve the gradient: <2t, -1/(t^2)> and at t=2 the point is (4, 1/4).
    and the gradient normal to t=2 is <4,-1/4>.

    So would the parametric equation be (4,1/4) +t<4,-1/4> ?

    Just Checking....
    Thanks a lot in advance!
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  2. #2
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    The point (1,1,0) is on the line.
    Therefore, the vector <1,1,0> is in the plane.
    Thus the normal is <1,1,0>\times <1,-1,2>.
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  3. #3
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    Great! And do you think my second problem is correct/ following the correct steps?
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