Question 1c Math 1
Download as DOCX, PDF0 likes367 views
The document calculates the divergence and curl of the vector field 퐹 = (푧2푒−푥)푖 + (푦3푙푛푧)푗 + (푥푒−푦)푘. The divergence is calculated to be -푧2푒−푥 + 3푦2푙푛푧 + 0. The curl is calculated to be (-푦푥푒−푦 - 푦3/푧)푖 - (푒−
1 of 1
Download to read offline
Question 1c Math 1
- 1. 1) c) Find the divergence and the curl of the vector field. 퐹 = (푧2푒−푥 )푖 + (푦3푙푛푧)푗 + (푥푒−푦 )푘 ∇. 푉 = 푑푉1 푑푥 + 푑푉2 푑푦 + 푑푉3 푑푧 = −푧2푒−푥 + 3푦2푙푛푧 + 0 퐶푢푟푙 푉 = ∇ × 푣 = || 푖 푗 푘 푑푉1 푑푉2 푑푥 푑푦 푑푉3 푑푧 푧2푒−푥 푦3푙푛푧 푥푒−푦 || = ( 푑푥푒−푦 푑푦 − 푑푦3푙푛푧 푑푧 푑푥푒−푦 푑푥 ) 푖 − ( − 푑푧2푒−푥 푑푧 ) 푗 + ( 푑푦3푙푛푧 푑푥 − 푑푧2푒−푥 푑푦 ) 푘 = (−푦푥푒−푦 − 푦3 1 푧 ) 푖 − (푒−푦 − 2푧푒−푥 )푗 + (0) = (−푦푥푒−푦 − 푦3 푧 ) 푖 − (푒−푦 − 2푧푒−푥 )푗