Show that on the saddle surface z= xy the two vector fields (Vī+x² ± i+ y°, yvī+x² ±xvI+y°) are principal at each point. Check that they are orthogonal and tangent to M.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Show that on the saddle surface z= xy the two vector fields
(V1+x* + V1+ y, yvl+x + xV1+ y*)
are principal at each point. Check that they are orthogonal and tangent to M.
Transcribed Image Text:Show that on the saddle surface z= xy the two vector fields (V1+x* + V1+ y, yvl+x + xV1+ y*) are principal at each point. Check that they are orthogonal and tangent to M.
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