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Calculus and vectors

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1. Does the line (x-7)/3=(y+8)/6=(z+4)/5 and the point P(10,-2,1) determine a plane?

Answer: Yes, it is a plane because when I substituted the point P(10,-2,1) into the equation, I got the coordinates (1,1,1) If the coordinate became to be (0,0,0) then it wouldn't be a plane.

  • Calculus and vectors - ,

    L1: (x-7)/3=(y+8)/6=(z+4)/5
    When P(10,-2,1) is substituted into L1, we get 1=1=1 which means that P is on the line.
    To define a plane from a point and a line, the point must NOT lie on the line else the plane is undefined.

    So the answer is no, because the point P lies on the given line.

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