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Given the three points A (3,-3,5), B(-5, 2, -1), C (0, 0, 1), let: . L1 be the line through A parallel to 4 .P be the plane through B with normal 0 . 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:

Given the three points A (3,-3,5), B(-5, 2, -1), C (0, 0, 1), let: . L1 be the line through A parallel to 4 .P be the plane through B with normal 0 . 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:

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 13AEXP
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Given the three points A (3,-3,5), B(-5, 2, -1), C (0, 0, 1), let: . L1 be the line through A parallel to 4 . P be the plane through B with normal 0 . 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: (1) 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. 0.6800451689 (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. [-2,33,32] (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.
Transcribed Image Text:Given the three points A (3,-3,5), B(-5, 2, -1), C (0, 0, 1), let: . L1 be the line through A parallel to 4 . P be the plane through B with normal 0 . 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: (1) 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. 0.6800451689 (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. [-2,33,32] (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.
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