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The divergence of the vector field x2i + 2y3j + z4k at x =1 , y= 2, z = 3 is
Correct answer is '134'. Can you explain this answer?
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The divergence of the vector field x2i + 2y3j + z4k at x =1 , y= 2, z...
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The divergence of the vector field x2i + 2y3j + z4k at x =1 , y= 2, z...
Given Vector Field:
- F = x^2i + 2y^3j + z^4k
Calculation of Divergence:
- The divergence of a vector field F = Pi + Qj + Rk is given by div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z.
Substitute the given values:
- P = x^2, Q = 2y^3, R = z^4
- ∂P/∂x = 2x, ∂Q/∂y = 6y^2, ∂R/∂z = 4z^3
Calculate the divergence at x=1, y=2, z=3:
- ∂P/∂x = 2(1) = 2
- ∂Q/∂y = 6(2)^2 = 24
- ∂R/∂z = 4(3)^3 = 108
- div(F) = 2 + 24 + 108 = 134
Therefore, the divergence of the given vector field at x=1, y=2, z=3 is 134.
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The divergence of the vector field x2i + 2y3j + z4k at x =1 , y= 2, z = 3 isCorrect answer is '134'. Can you explain this answer?
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The divergence of the vector field x2i + 2y3j + z4k at x =1 , y= 2, z = 3 isCorrect answer is '134'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The divergence of the vector field x2i + 2y3j + z4k at x =1 , y= 2, z = 3 isCorrect answer is '134'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The divergence of the vector field x2i + 2y3j + z4k at x =1 , y= 2, z = 3 isCorrect answer is '134'. Can you explain this answer?.
The divergence of the vector field x2i + 2y3j + z4k at x =1 , y= 2, z = 3 isCorrect answer is '134'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The divergence of the vector field x2i + 2y3j + z4k at x =1 , y= 2, z = 3 isCorrect answer is '134'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The divergence of the vector field x2i + 2y3j + z4k at x =1 , y= 2, z = 3 isCorrect answer is '134'. Can you explain this answer?.
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