Consider the plane passing through the points (0,0,6), (1,0, - 12), and (1,7,6). Answer parts (a) through (c) below. . . . a. Find an equation of the plane. An equation for the plane is 126x -18y +7z -42=0. (Type an equation.) b. Find the intercepts of the plane with the three coordinate axes. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. (Type an integer or a fraction.) O A. The plane intersects the y-axis at (0, ,0) , and does not intersect the x-axis or the z-axis. O B. The plane intersects the y-axis at (0, 0 ,0) , the z-axis at (0,0, 6 ) , and does not intersect the x-axis. O C. The plane intersects the x-axis at ( ,0,0) , the z-axis at (0,0, ) and does not intersect the y-axis. O D. The plane intersects the z-axis at (0,0, and does not intersect the x-axis or the y-axis. O E. The plane intersects the x-axis at ( ,0,0) , the y-axis at (0, ,0) , and the z-axis at (0,0, ). O F. The plane intersects the x-axis at (0,0) , and does not intersect the y-axis or the z-axis. O G. The plane intersects the x-axis at ( ,0,0) , the y-axis at (0, ,0) , and does not intersect the z-axis.Find an equation of the following plane. The plane containing the lines x=4 +t,y=5-4t,z=1 and x=3s, y=9s, z=6 - 5s, if possible. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. @ A. An equation for the plane is [20x + S5y+21z2-126=0|. (Type an equation.) () B. The plane does not exist. Consider the plane passing through the points (0,0,6), (1,0, - 12), and (1,7,6). Answer parts (a) through (c) below. Um. Ine plane intersects ine y-axis at ( U, ,) , and does not intersect the x-axis or ine z-axis. O B. The plane intersects the y-axis at (0, ,0) , the z-axis at (0,0, ) , and does not intersect the x-axis. O C. The plane intersects the x-axis at ( ,0,0) , the z-axis at (0,0, ) and does not intersect the y-axis. O D. The plane intersects the z-axis at (0,0, ) and does not intersect the x-axis or the y-axis. CE. The plane intersects the x-axis at .0,0 , the y-axis at |0, - 3 ,0 , and the z-axis at (0, 0, 6 ) . O F. The plane intersects the x-axis at ( ,0,0) , and does not intersect the y-axis or the z-axis. O G. The plane intersects the x-axis at ( ,0,0) , the y-axis at (0, ,0) , and does not intersect the z-axis. c. Make a sketch of the plane. Choose the correct answer below. Note that the graphs are not to scale. O A. O B. O c. OD. N (0,0,6) (0.0,- (0,0,6) 5:0,0X 0, - 7,0 7 X (0,6,0) 73,0,0 0,0