Find parametric equations of the line that passes through the center of the sphere

x ^2+ y - 14 y^2 + 53 + z^2 + 4 z = 1

and is perpendicular to the plane

10 x - 6 y + 7 z = -1

.

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The freaking computer keeps telling me that my normal vector and equations of the line are incorrect. Here is what i currently have.

DirectionVector:= [10*x,-6*y,7*z];

EquationsOfLine:= [10*t,7-6*t,-2+7*t];