Given the three points A (5, 1,-4), B (-5, 1, -3), C (-3,4,-5), let: . L1...

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Given the three points A (5, 1,-4), B (-5, 1, -3), C (-3,4,-5), let: . L1 be the line through A parallel to . P be the plane through B with normal 5 2 2 2 . E be the point of intersection of L1 and P, . S be the sphere through A, B, C, E, . F be the centre of S, . L2 be the line through C and F. Using the geom3d package, or otherwise: (i) Find a decimal approximation to the angle between L1 and P, correct to 10 significant figures. Enter your answer in the box below. To prevent typing errors you can copy and paste the answer from your Maple worksheet. (ii) Find the coordinates of F and enter them in the box below. You should enclose the coordinates with square brackets, eg [1,2,3], and your answer should be exact, ie not a decimal approximation. To prevent typing errors you can copy and paste the answer from your Maple worksheet. (iii) Find the distance between A and L2. Your answer should be exact, not a decimal approximation. Enter your answer in the box below using Maple syntax. To prevent typing errors you can copy and paste the answer from your Maple worksheet. Ay Given the three points A (5, 1,-4), B (-5, 1, -3), C (-3,4,-5), let: . L1 be the line through A parallel to . P be the plane through B with normal 5 2 2 2 . E be the point of intersection of L1 and P, . S be the sphere through A, B, C, E, . F be the centre of S, . L2 be the line through C and F. Using the geom3d package, or otherwise: (i) Find a decimal approximation to the angle between L1 and P, correct to 10 significant figures. Enter your answer in the box below. To prevent typing errors you can copy and paste the answer from your Maple worksheet. (ii) Find the coordinates of F and enter them in the box below. You should enclose the coordinates with square brackets, eg [1,2,3], and your answer should be exact, ie not a decimal approximation. To prevent typing errors you can copy and paste the answer from your Maple worksheet. (iii) Find the distance between A and L2. Your answer should be exact, not a decimal approximation. Enter your answer in the box below using Maple syntax. To prevent typing errors you can copy and paste the answer from your Maple worksheet. Ay

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The image contains a problem that requires answering three questions related to threedimensional geometry The problem involves points lines planes and ... View the full answer