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(b) A surface, S, is given by f(r) = x²y + y²z + z²x = 4. Confirm that the point with position vector a lies on both the surface S and the plane P and find the angle of intersection between S and P at that point. Hint: consider the normals to the surface and plane at this point.

(b) A surface, S, is given by f(r) = x²y + y²z + z²x = 4. Confirm that the point with position vector a lies on both the surface S and the plane P and find the angle of intersection between S and P at that point. Hint: consider the normals to the surface and plane at this point.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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(b) A surface, S, is given by f(r) = x²y + y²z + z²x = 4. Confirm that the point with position vector a lies on both the surface S and the plane P and find the angle of intersection between S and P at that point. Hint: consider the normals to the surface and plane at this point.
Transcribed Image Text:(b) A surface, S, is given by f(r) = x²y + y²z + z²x = 4. Confirm that the point with position vector a lies on both the surface S and the plane P and find the angle of intersection between S and P at that point. Hint: consider the normals to the surface and plane at this point.
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