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points to find the equation of the plane. Explain why three collinear points do not determine a unique plane Explain why a line C and a point P not on C determine a unique plane. Explain how you would use the equation of C and the coordinates P to find the equation of the plane. Explain why P and C do not determine a unique plane if P is on C. y. 10. Explain why two intersecting lines determine a unique plane. Explain how you would use the equations of the lines to find the equation of the plane. Explain why two distinct parallel lines determine a unique a 11. plane. Explain how you would use the equations of the ines to find the equation of the plane. , 12.丿Explain why two skew lines do not determine a plane. 13. Explain why any two skew lines lie on a unique pair of parallel planes. 14. The angle θ between two intersecting planes, called the dihedral angle, is defined to be the angle between the two normal vectors to the planes, where ã. θ = cos-1 INillNll 1 N1 N2 Draw a figure that illustrates the dihedral angle and ex- plain why the definition given is a reasonable definition. 15. Given the equations for a line C and for a plane P, explain how to determine whether C is orthogonal to P. 16. Explain how to tell when two planes are perpendicular. 17. When a line L intersects a plane P the angle between them is defined to be the complement of the acute angle between the direction vector for the line and the n vector to the plane. Draw a figure that illustrates this an- gle, and explain definition ormal gle and explain why the definition given is in the derivations of the formulas i from a point