Q. 24 Compute聽the聽curl聽of聽the聽vec... [FREE SOLUTION]

91影视

Chapter 14: Q. 24 (page 1132)

$C o m p u t e t h e c u r l o f t h e v e c t o r f i e l d s i n E x e r c i s e s 23 鈥� 28 . G (x, y, z) = (x^{2} + y 鈭� z) i 鈭� 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k$

Short Answer

Expert verified

$curl G = = (2 {ye}^{x^{2} + y^{2} + z^{2}} - 2 y sinz) i + 2 {xe}^{x^{2} + y^{2} + z^{2}} j - k$

Step by step solution

Step 1. Given information is:

$G (x, y, z) = (x^{2} + y 鈭� z) i 鈭� 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k$

Step 2. Curl of vector field

$Here, G (x, y, z) = (x^{2} + y 鈭� z) i 鈭� 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k Compare this with, G (x, y, z) = g_{1} (x, y, z) i + g_{2} (x, y, z) j + g_{3} (x, y, z) k Then, g_{1} (x, y, z) = x^{2} + y 鈭� z, g_{2} (x, y, z) = 鈭� 2 y \cos z, g_{3} (x, y, z) = e^{x^{2} + y^{2} + z^{2}} Now, curl G = |\begin{matrix} i & j & k \\ \frac{鈭�}{鈭� x} & \frac{鈭�}{鈭� y} & \frac{鈭�}{鈭� z} \\ x^{2} + y 鈭� z & 鈭� 2 y \cos z & e^{x^{2} + y^{2} + z^{2}} \end{matrix}| = i (\frac{鈭� (e^{x^{2} + y^{2} + z^{2}})}{鈭� y} - \frac{鈭� (鈭� 2 y \cos z)}{鈭� z}) + j (\frac{鈭� (x^{2} + y 鈭� z)}{鈭� z} - \frac{鈭� (e^{x^{2} + y^{2} + z^{2}})}{鈭� x}) + k (\frac{鈭� (鈭� 2 y \cos z)}{鈭� x} - \frac{鈭� (x^{2} + y 鈭� z)}{鈭� y}) = (2 {ye}^{x^{2} + y^{2} + z^{2}} - 2 y sinz) i + 2 {xe}^{x^{2} + y^{2} + z^{2}} j - k$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

$C o m p u t e t h e c u r l o f t h e v e c t o r f i e l d s i n E x e r c i s e s 23 鈥� 28 . G (x, y, z) = (x^{2} + y 鈭� z) i 鈭� 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Curl of vector field

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Statistics

Calculus

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

91影视

ComputethecurlofthevectorfieldsinExercises23鈥�28.G(x,y,z)=(x2+y鈭�z)i鈭�2ycoszj+ex2+y2+z2k

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Curl of vector field

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Statistics

Calculus

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

$C o m p u t e t h e c u r l o f t h e v e c t o r f i e l d s i n E x e r c i s e s 23 鈥� 28 . G (x, y, z) = (x^{2} + y 鈭� z) i 鈭� 2 y \cos zj + e^{x^{2} + y^{2} + z^{2}} k$