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Math Help - find the distance, find the point

  1. #1
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    Red face find the distance, find the point

    Please Help!


    Find the point P where the line x=1+t y=2t z=-3t intersects the plane x+y-z=-2

    Find the distance from the point (-1,2,3) to the plane -1x+0y-2z=5
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  2. #2
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    Quote Originally Posted by karnold9 View Post
    Please Help!


    Find the point P where the line x=1+t y=2t z=-3t intersects the plane x+y-z=-2

    Find the distance from the point (-1,2,3) to the plane -1x+0y-2z=5
    plug x,y,z into the equation of the plane to get

    (1+t)+(2t)-(-3t)=-2 \iff 6t+1=-2 \iff t=-\frac{1}{2}

    Plug this value into the parametric equation to find the point.

    for part b write the plane is this form

    ax+by+cz+d=0 and use the formula from this link

    Point-Plane Distance -- from Wolfram MathWorld

    I hope this helps.
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