4. Determine if the parallel lines in each pair are distinct or coincident. a) [x, y,...

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4. Determine if the parallel lines in each pair are distinct or coincident. a) [x, y, z]=[5, 1, 3]+s[2, 1, 7] [x, y, z]=[2, 3, 9]+[2, 1, 7] b) [x, y, z]-[4, 1, 0]+s[3, -5, 6] [x, y, z]=[13, 14, 18]+[-3, 5, -6] c) [x, y, z]=[5, 1, 3]+s[1, 4, -1] [x, y, z]=[3,-7, 5]+[-2, -8,2] d) [x, y, z]=[4,8, 0]+s[7, 21, 14] [x, y, z]=[25, 55, 42]+[8,-24, 16] 5. Determine if the lines in each pair intersect. If so, find the coordinates of the point of intersection. a) [x, y, z]=[6, 5,14]+s[1, 1, 3] [x, y, z] [11, 0, -17]+[4, -1, -6] b) [x, y, z]-[3,-2, 2]+s[-1, -2, 0] [x, y, z] [1, 0, -1]+[0, 2, 3] c) [x, y, z]=[7, 0, -15]+s[2, 1, -5] [x, y, z] [-7,-7, 20]+[2, 1, -5] d) [x, y, z] [8,-1, 8]+s[2, -3, 0] [x, y, z] = [1, 20, 0]+[1, -5, 3] 6. Determine if the non-parallel lines in each pair are skew. a) [x, y, z]=[4, 7, -1]+s[-2, 1, 2] [x, y, z]=[1, 3, -1]+t[4, 1, 2] b) [x, y, z]=[6, 2, 1]+s[6, 18, -6] [x, y, z]=[7, 13, 1]+[6, 1, 2] c) [x, y, z]=[2, 4, 2]+s[2, 1, -5] [x, y, z]=[4, 3, 7]+[2, 1, 5] d) [x, y, z]=[-6, 12, 8]+s[2, 1, 5] [x, y, z]=[8,9,7]+[2, 1, 5] e) [x, y, z]=[5, 4, 1]+s[6, 4, 2] [x, y, z]=[2, 3, 4]+[1, 2, 3] f) [x, y, z]=[1, -1, 0]+s[2, 1, 3] [x, y, z]=[1, 2, 3]+[3, 2, 4] 4. Determine if the parallel lines in each pair are distinct or coincident. a) [x, y, z]=[5, 1, 3]+s[2, 1, 7] [x, y, z]=[2, 3, 9]+[2, 1, 7] b) [x, y, z]-[4, 1, 0]+s[3, -5, 6] [x, y, z]=[13, 14, 18]+[-3, 5, -6] c) [x, y, z]=[5, 1, 3]+s[1, 4, -1] [x, y, z]=[3,-7, 5]+[-2, -8,2] d) [x, y, z]=[4,8, 0]+s[7, 21, 14] [x, y, z]=[25, 55, 42]+[8,-24, 16] 5. Determine if the lines in each pair intersect. If so, find the coordinates of the point of intersection. a) [x, y, z]=[6, 5,14]+s[1, 1, 3] [x, y, z] [11, 0, -17]+[4, -1, -6] b) [x, y, z]-[3,-2, 2]+s[-1, -2, 0] [x, y, z] [1, 0, -1]+[0, 2, 3] c) [x, y, z]=[7, 0, -15]+s[2, 1, -5] [x, y, z] [-7,-7, 20]+[2, 1, -5] d) [x, y, z] [8,-1, 8]+s[2, -3, 0] [x, y, z] = [1, 20, 0]+[1, -5, 3] 6. Determine if the non-parallel lines in each pair are skew. a) [x, y, z]=[4, 7, -1]+s[-2, 1, 2] [x, y, z]=[1, 3, -1]+t[4, 1, 2] b) [x, y, z]=[6, 2, 1]+s[6, 18, -6] [x, y, z]=[7, 13, 1]+[6, 1, 2] c) [x, y, z]=[2, 4, 2]+s[2, 1, -5] [x, y, z]=[4, 3, 7]+[2, 1, 5] d) [x, y, z]=[-6, 12, 8]+s[2, 1, 5] [x, y, z]=[8,9,7]+[2, 1, 5] e) [x, y, z]=[5, 4, 1]+s[6, 4, 2] [x, y, z]=[2, 3, 4]+[1, 2, 3] f) [x, y, z]=[1, -1, 0]+s[2, 1, 3] [x, y, z]=[1, 2, 3]+[3, 2, 4]