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find the equation of plane passing through point(0,7,-7) and containing line x+1/-3=y-3/2=z+2/1

  • maths -

    I assume you mean
    (x+1)/-3 = (y-3)/2 = (z+2)/1 , the brackets are essential
    so we know (-1,3,-2) is a point on the plane and we also have a direction vector of [-3,2,1]
    using (0,7,-7) we can find a second direction vector which would be
    [1,4,-5]
    a normal to [-3,2,1] and [1,4,-5] is [-14, -14 , -14]
    or reduced to [1,1,1]

    So the equation of the plane is
    x + y + z = c, but -1,3,-2) lies on it
    -1 + 3 - 2 = c = 0

    equation of plane:
    x+y+z = 0

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