Answer Happy

Given the three points A(3, -2, 3), B(7, 1, 7), C(17, 15, 15), let: S1 be the sphere with centre A and radius 12, S2 be the sphere which has the line segment BC as a diameter, T be the circle of intersection of S1 and S2, W . a . . . E be the centre of T, L1 be the line through B and E, L2 be the line through A parallel to 1 (-) 2 Using the geom3d package, or otherwise: (i) Find the coordinates of E 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. (ii) Find a decimal approximation to the angle (in radians) between L1 and L2. Your answer should be correct to 10 significant figures. Enter your answer in the box below. (iii) Find the distance between L1 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.