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  1. #1
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    Intersect

    find the value of k such that the line x-1 = y-2 = z-k and the plane
    3 1 5
    2x-y-z+10 = 0 intersect only at one pin .
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by fastman390 View Post
    find the value of k such that the line x-1 = y-2 = z-k and the plane
    3 1 5
    2x-y-z+10 = 0 intersect only at one pin .
    I don't have time for a full solution,but try this

    converted the symmetric equations into parametric form and sub into the equation of the plane. see what happens

    Good luck.
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  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by fastman390 View Post
    find the value of k such that the line x-1 = y-2 = z-k and the plane
    3 1 5
    2x-y-z+10 = 0 intersect only at one pin .
    we have that
    \frac{x-1}{3}=\frac{y-2}{1}=\frac{z-k}{5}

    setting each equal to t we can get the parametric form.

    \frac{x-1}{3}=t \iff x=3t+1

    doing the same for the others gives

    y=t+2 \mbox{ and } z=5t+k

    plugging these into the equation of the plane gives
    2(3t+1)-(t+2)-(5t+k)+10=0 \iff -k+10 =0 \iff k=10
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