Find the divergence of each of the following vector fields at all points where they are defined. (a) div(x(x2 y2 z2)1.5i y(x2 y2 z2)1.5j z(x2 y2 z2)1.5k)

the divergence of the vector fields at all points its defined is 0

Step-by-step explanation:

Given that;

div ( [x / (x²+ y² + z²)^1.5]i  +  [y / (x² + y² + z²)^1.5]j  +  [z / (x² + y² + z²)^1.5]k )

= d/dx [x / (x²+ y² + z²)^1.5]  +  d/dx [y / (x² + y² + z²)^1.5] +  d/dx [z / (x² + y² + z²)^1.5]

= [1 / (x²+ y² + z²)^1.5] - [3x² / (x²+ y² + z²)^2.5] + [1 / (x²+ y² + z²)^1.5] - [3y² / (x²+ y² + z²)^2.5] + [1 / (x²+ y² + z²)^1.5] - [3z² / (x²+ y² + z²)^2.5]

= [3 / (x²+ y² + z²)^1.5]  -  [(3x² + 3y² +3z²) / (x²+ y² + z²)^2.5]

= [2 / (x²+ y² + z²)^1.5]   -   [3 / (x²+ y² + z²)^1.5]  = 0

therefore the divergence of the vector fields at all points its defined is 0

answer:      

step-by-step explanation:

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step-by-step explanation: