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Name: _____________________________________ Extra Section 9.5 Practice - OPTIONAL Match the four different representations (one from Category A, one from Category B, one from Category C, and one from Category D) for the same line. Do this for all seven lines. Category A The line between (0, 0, 1) and (1, 2, 1) Category B r = 9,6, 7 + t -3,-2,-1 The line between (0, 0, 4) and (12, 8, 8) r = 3,3,3 + t 7,1,2 The line between (0, -3, 3) and (3, 3, 0) r = 2, 4,1 + t 1, 2, 0 The line between (5, 0, 7) and (-2, -7, 0) r = 3,-2,5 + t -1,-1,-1 The line between (-4, 2, 1) and (-11, 1, -1) r = 0,0,0 + t -1,1,-3 The line between (-3, 3, -9) and (3, -3, 9) r = 1,2, 3 + t 0,-1,1 The line between (1, 3, 2) and (1, -1, 6) r = 1,-1,2 + t 1,2,-1 Category C x=2+t y = 1 + 2t z=1–t x = 10 + 7t y=4+t z = 5 + 2t x = 2 – 2t y = -3 – 2t z = 4 – 2t x = -1 + t y=1-t z = -3 + 3t x = 2t y = 4t z=1 x=1 y = -t z=5+t x = 6 – 6t y = 4 – 4t z = 6 – 2t Category D x + 4 y - 2 z -1 = = 14 2 4 x-3 y-2 z-5 = = 3 2 1 x -1 y - 2 = ,z =1 2 4 x -1 y +1 z - 2 = = 2 4 -2 x = 1, y -1 z - 4 = -2 2 x y+5 z-2 = = 2 2 2 x+2 y-2 z+6 = = -2 2 -6 Consider the point (11, 3, 8) in R3. Find an equation of a line that contains your point and the origin. Find an equation of a line that contains your point and the point (1, -1, 1) Now find an equation of the plane that contains the two lines that you’ve just found. Find an equation of the plane that contains your point and is perpendicular to the x-axis. Find an equation of the plane that contains your point and is perpendicular to the line y=x in the xyplane. Finally, find an equation of a plane that does NOT contain your point. Consider the following set of three points: (-1, 4, 2), (3, 1, 1), (7, -2, 0). Find a parametric equation of the unique plane containing these points.