A, B, C, D, E and O, as shown in the following figure z Is3:x? = 16 – 4z P S=ƏQ S4: x = 0 S5: y = 0 S6: z = 0 $2:2y = 6 – x O(0.0.0) is the origin and is hidden B S1:2x – 4y + z = 4 E)þetermine the normal vector of the surfaces S1, S2 and S3 at an arbitrary point P (x, y, z) belonging to each of the surfaces. To do this, use the parametrization of the surfaces and deriving in the first parameter and deriving in the second parameter, calculate the director vectors of the tangent lines in P and taking the vector product of these director vectors, calculate N the normal vector to the surfaces S1, S2 and S3.
A, B, C, D, E and O, as shown in the following figure z Is3:x? = 16 – 4z P S=ƏQ S4: x = 0 S5: y = 0 S6: z = 0 $2:2y = 6 – x O(0.0.0) is the origin and is hidden B S1:2x – 4y + z = 4 E)þetermine the normal vector of the surfaces S1, S2 and S3 at an arbitrary point P (x, y, z) belonging to each of the surfaces. To do this, use the parametrization of the surfaces and deriving in the first parameter and deriving in the second parameter, calculate the director vectors of the tangent lines in P and taking the vector product of these director vectors, calculate N the normal vector to the surfaces S1, S2 and S3.
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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Question
E) Answer the question shown in the image
Transcribed Image Text:Consider the solid bounded by surfaces S1, S2, S3, S4, S5, and S6 with vertices
A, B, C, D, E and O, as shown in the following figure
S3:x2 = 16 – 4z
LE
P S=ƏQ
S4: x = 0
S5: y = 0
S6: z = 0
$2:2y = 6 – x
O(0.0.0) is the origin and is hidden
B
S1:2x – 4y +z =4
E)betermine the normal vector of the surfaces S1, S2 and S3 at an arbitrary
point P (x, y, z) belonging to each of the surfaces. To do this, use the
parametrization of the surfaces and deriving in the first parameter and
deriving in the second parameter, calculate the director vectors of the
tangent lines in P and taking the vector product of these director vectors,
calculate N the normal vector to the surfaces S1, S2 and S3.
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