The divergence of the vector field F⃗ =(x+3y)i^+(y−3z)j^+(x−2z)k^𝐹→=(𝑥+3𝑦)𝑖^+(𝑦−3𝑧)𝑗^+(𝑥−2𝑧)𝑘^ isa.None of theseb.0c.2d.-2

Question

The divergence of the vector field F⃗ =(x+3y)i^+(y−3z)j^+(x−2z)k^𝐹→=(𝑥+3𝑦)𝑖^+(𝑦−3𝑧)𝑗^+(𝑥−2𝑧)𝑘^ isa.None of theseb.0c.2d.-2
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Solution 1

The divergence of a vector field F = P(x,y,z)i + Q(x,y,z)j + R(x,y,z)k is given by the formula:

div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z

Here, P(x,y,z) = x + 3y, Q(x,y,z) = y - 3z, and R(x,y,z) = x - 2z.

So, we have:

∂P/∂x = ∂/∂x (x + 3y) = 1 (since the derivative of x with respect to x is 1 and the deriva Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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