The divergence of the vector function G(x, y, z) is given by div. G D.G C where, V = 2n + 3y on + ka dz The Rotational of the function C(M,y, 2) is defined by Curl G = VXG where = 23+3% +k²/ J. on In the given question G(x, y, z)=(5 Castely z2²)i +(3e" sim(y) z³)j- (ryz¹) k (a) divergence of the function ! div. G = (12 +13 +K 2₂). [(5 cos(x) y ₂²) ² + (3 en sin(y) z ³ ) ³ - (my z"¹) k] div.G₁ = 2 5 Cas(x) y ₂² +2(3 e^ Sin (y)z ³) - 2₂ (my z²¹) бу P 2:1·i = 3.j = k·k=) ( S 23-3K = k·i = 0 div. G = 5 sinen) yz² + 3 em casy) z³ + xy at the point (1.1.1) div. G = -5.Sin(1). 1. (11² + 3. C. Cos(1) (13²³ + 1*1 div. G -5 Sim1 + 3 e cas 1 + 1
The divergence of the vector function G(x, y, z) is given by div. G D.G C where, V = 2n + 3y on + ka dz The Rotational of the function C(M,y, 2) is defined by Curl G = VXG where = 23+3% +k²/ J. on In the given question G(x, y, z)=(5 Castely z2²)i +(3e" sim(y) z³)j- (ryz¹) k (a) divergence of the function ! div. G = (12 +13 +K 2₂). [(5 cos(x) y ₂²) ² + (3 en sin(y) z ³ ) ³ - (my z"¹) k] div.G₁ = 2 5 Cas(x) y ₂² +2(3 e^ Sin (y)z ³) - 2₂ (my z²¹) бу P 2:1·i = 3.j = k·k=) ( S 23-3K = k·i = 0 div. G = 5 sinen) yz² + 3 em casy) z³ + xy at the point (1.1.1) div. G = -5.Sin(1). 1. (11² + 3. C. Cos(1) (13²³ + 1*1 div. G -5 Sim1 + 3 e cas 1 + 1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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![The divergence of the vector function
G(x, y, z) is given by
2)
div. G = D.G
where √ = 13
an
2
1.
go by
y, is
The Rotational of the function (1.7, 2) és
defined by
Curl G = X X G
where,
In
az
4
+7 by + k₂
az
· p p p p
s
In the given question
G(x, y, z) = (5 Casta) y z²¹)i +(3e" ain(y)2³) 3 - (my z¹) R
(nyz¹) k
(a) divergence of the function!
div. G = ( 12 +13y + ko/₂). [(5 Cox(x) y 2²) ₁ +
(3 e ³ Sin(y) z ³) ³ - (my z "¹) k]
en
div.G.
DZ
•dr.G₁ = 2 5 cm () y z² + 2 (3 e* & (y) Z³) - 2 (x y z ")
бу
div. G = — 5 sin (m) y z² + 3 en casy z ²³ +
div. G
:ii-3.j= k·k=) (
· Ĵ = 1·K = k·i = 0
=
+ xy
-5 Sim1 + 3e cas 1 + 1
~
at the point (1.1.1)
div. G = - 5. Sin (1). 1. (1³² + 3. e · Cas ( 1) (1)³² + 1 + 1
e'.
12
old
₂²
Z](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39cdee93-e28a-4e21-8715-0dbf90412314%2Fed4daaa6-e0fe-4265-ae7a-e900f191eca4%2F7hvn3xl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The divergence of the vector function
G(x, y, z) is given by
2)
div. G = D.G
where √ = 13
an
2
1.
go by
y, is
The Rotational of the function (1.7, 2) és
defined by
Curl G = X X G
where,
In
az
4
+7 by + k₂
az
· p p p p
s
In the given question
G(x, y, z) = (5 Casta) y z²¹)i +(3e" ain(y)2³) 3 - (my z¹) R
(nyz¹) k
(a) divergence of the function!
div. G = ( 12 +13y + ko/₂). [(5 Cox(x) y 2²) ₁ +
(3 e ³ Sin(y) z ³) ³ - (my z "¹) k]
en
div.G.
DZ
•dr.G₁ = 2 5 cm () y z² + 2 (3 e* & (y) Z³) - 2 (x y z ")
бу
div. G = — 5 sin (m) y z² + 3 en casy z ²³ +
div. G
:ii-3.j= k·k=) (
· Ĵ = 1·K = k·i = 0
=
+ xy
-5 Sim1 + 3e cas 1 + 1
~
at the point (1.1.1)
div. G = - 5. Sin (1). 1. (1³² + 3. e · Cas ( 1) (1)³² + 1 + 1
e'.
12
old
₂²
Z
![(1) Rotational function ?
Curl G₂ = XX G
x
= (1 +1³ +K ² ) x [(sy z²casx)i + (se^z^² siny) j
- (ny z¹) K]
olă
j
ว
xola
Ə
by
5y2²(am 3e" 2²siny - (ny-z¹)
ny
z
dz
i [3₂ (-rye) - 3₂ (30^-2²x^y)]- 5 [3 (nye¹)-2 (6)
+ K [3 (36²2 ³any) - By (5 y 2² (asx)]
i [-22¹-96¹2² smy] - j[-yz¹ - loy z Cas x]
+K [3²² 2²³ ³y - 52² cass"]
at (1, 1, 1) Rotational function is obtained as,
Curl G = (-1-gesin1) + (1+10 Cus 1)3 + (3 ent-cast
Hence,
The divergence of the given function G(x,y,z)
at the point (1,1,1) is
div. G₂ = 1-5 Sim1 + 3 e cas 1
The rotational function of the given function
G(x, y, 2) at the point (1.1.1) is
Сиал а
@ims) i + (1 + 10 Cas 1) 5+ (3esin1-56m) K
j](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39cdee93-e28a-4e21-8715-0dbf90412314%2Fed4daaa6-e0fe-4265-ae7a-e900f191eca4%2Fa99qomk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(1) Rotational function ?
Curl G₂ = XX G
x
= (1 +1³ +K ² ) x [(sy z²casx)i + (se^z^² siny) j
- (ny z¹) K]
olă
j
ว
xola
Ə
by
5y2²(am 3e" 2²siny - (ny-z¹)
ny
z
dz
i [3₂ (-rye) - 3₂ (30^-2²x^y)]- 5 [3 (nye¹)-2 (6)
+ K [3 (36²2 ³any) - By (5 y 2² (asx)]
i [-22¹-96¹2² smy] - j[-yz¹ - loy z Cas x]
+K [3²² 2²³ ³y - 52² cass"]
at (1, 1, 1) Rotational function is obtained as,
Curl G = (-1-gesin1) + (1+10 Cus 1)3 + (3 ent-cast
Hence,
The divergence of the given function G(x,y,z)
at the point (1,1,1) is
div. G₂ = 1-5 Sim1 + 3 e cas 1
The rotational function of the given function
G(x, y, 2) at the point (1.1.1) is
Сиал а
@ims) i + (1 + 10 Cas 1) 5+ (3esin1-56m) K
j
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