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Intersection of a Line and a Plane in 3-Space Activity1.a.Line is intersected at the point (3, -7,5) so: Line should not be parallel to the plane (3, -7,5) lies on the plane (a^i+b^j+c^k).(−2^i+4^j+7^k)≠0−2a+4b+7c ≠03a−7b−5c=dEquationof planeisax+by+cz=3a−7b−5c withcondition of2a−4b−7c≠0
b.Plane ins not intersected by the line Line is parallel to plane Normal vector of the plane is perpendicular to line vector−2a+4b+7c=0ax+by+cz=disequationof plane with condition−2a+4b+7c=0c.Plane that the line lies on Point (1, -3,2) lies on the plane .(−2^i+4^j+7^k)is perpendicular to normal vectora−3b+2c=d−2a+4b+7c=0Equationof planeisax+by+cz=a−3b+2cwith condition−2a+4b+7c=0