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
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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Needed to be solved first three part only .
Please solve completely and get the thumbs up. Please show neat and clean work with correct solution
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d1f3ce4-4054-4b62-a653-883caa68d0b4%2F9dd80503-f8c6-4a11-a8cc-07971e42e8c2%2Fvr40pai_processed.jpeg&w=3840&q=75)
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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