Math Problem Statement

Adjuk meg az A = [3,2,2], B = [4,3,3], C = [5,-1,5], D = [6,0,6] paralelogrammán a v(r) = [x * y, y, z^2, z^3] vektor-vektorfüggvénnyel megadott vektormező integrálját, ahol a felületi normális a AB × AC irányába áll.

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Calculus
Surface Integrals
Cross Product

Formulas

Cross Product Formula: AB × AC
Surface Integral of a Vector Field: ∬_S v(r) · n dS

Theorems

Fundamentals of Surface Integrals
Vector Field and Normal Direction Calculation

Suitable Grade Level

University Level (Advanced Mathematics)

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