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what are the conditions when a line and plane intersects?

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To find the intersection point P(x,y,z), substitute line parametric values of x, y and z into the plane equation:

A(x1 + at) + B(y1 + bt) + C(z1 + ct) + D = 0

A line will be parallel to the plane if:  

aA + bB + cC = 0

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