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Figure 1 shows the contour surface G = 6 where G(x, y, z) = x² - y² + 3z². On the sur- face is point P (red dot) at (2, 1, -1), and through P we see the tangent plane (green surface), cross-section at x = 2 (blue line), unit normal vector (black arrow), and nor- mal line (dashed line). 2/7 0 Figure 1 i) Compute the gradient of G at P. ii) Compute the unit normal vector n at P. iii) Compute the tangent plane at P using the plane equation (ra) n = 0. -2 Z ****** 0

Figure 1 shows the contour surface G = 6 where G(x, y, z) = x² - y² + 3z². On the sur- face is point P (red dot) at (2, 1, -1), and through P we see the tangent plane (green surface), cross-section at x = 2 (blue line), unit normal vector (black arrow), and nor- mal line (dashed line). 2/7 0 Figure 1 i) Compute the gradient of G at P. ii) Compute the unit normal vector n at P. iii) Compute the tangent plane at P using the plane equation (ra) n = 0. -2 Z ****** 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 97E
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Question 1 Figure 1 shows the contour surface G = 6 where G(x, y, z) = x² - y² + 3z². On the sur- face is point P (red dot) at (2, 1,-1), and through P we see the tangent plane (green surface), cross-section at x = 2 (blue line), unit normal vector (black arrow), and nor- mal line (dashed line). BATTTTTTT 2 0 2/7 X Figure 1 i) Compute the gradient of G at P. ii) Compute the unit normal vector n at P. iii) Compute the tangent plane at P using the plane equation (r- a) n = 0.
Transcribed Image Text:Question 1 Figure 1 shows the contour surface G = 6 where G(x, y, z) = x² - y² + 3z². On the sur- face is point P (red dot) at (2, 1,-1), and through P we see the tangent plane (green surface), cross-section at x = 2 (blue line), unit normal vector (black arrow), and nor- mal line (dashed line). BATTTTTTT 2 0 2/7 X Figure 1 i) Compute the gradient of G at P. ii) Compute the unit normal vector n at P. iii) Compute the tangent plane at P using the plane equation (r- a) n = 0.
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