(a) Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the given point. O X-3- y + 1 Z- 10 Ox-3=y+1 = z - 10 y+1 z-10 -6 X-3 %3D %3D X - 3 6 y+ 1 -2 Z- 10 -1 !! %3D X-3 6. y+1 Z- 10 (b) Find the cosine of the angle between the gradient vectors at this point. cos(e) = 90 %3! State whether or not the surfaces are orthogonal at the point of intersection.
(a) Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the given point. O X-3- y + 1 Z- 10 Ox-3=y+1 = z - 10 y+1 z-10 -6 X-3 %3D %3D X - 3 6 y+ 1 -2 Z- 10 -1 !! %3D X-3 6. y+1 Z- 10 (b) Find the cosine of the angle between the gradient vectors at this point. cos(e) = 90 %3! State whether or not the surfaces are orthogonal at the point of intersection.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the following.
z = x? + y?, z= 9- y,
z = 9 - y,
(3,-1, 10)
(a) Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the given point.
O X- 3 - Y + 1
Z- 10
6.
Ox-3=y+ 1 = z - 10
|
X - 3 y+ 1_z- 10
y + 1 z- 10
%3D
1
-6
X -3 y+1
N- 10
-1
%3D
%3D
6.
-2
X-3-y+ 1 - z - 10
6.
%3D
%3D
6.
(b) Find the cosine of the angle between the gradient vectors at this point.
cos(0) = 90
%3D
State whether or not the surfaces are. orthogonal at the point of intersection.
Yes, they are orthogonal.
No, they are not orthogonal.
N.
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