GATE Civil Engineering 2023 (Set 2): Identity for div(φu) - Scalar & Vector Field Divergence

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Civil Engineering > GATE 2023 SET-2 > Vector Calculus

Let φ be a scalar field, and u be a vector field. Which of the following identities is true for div(φu)?

A

div(φu) = φdiv(u) + u ⋅ grad(φ)

B

div(φu) = φdiv(u) + u × grad(φ)

C

div(φu) = φgrad(u) + u ⋅ grad(φ)

D

div(φu) = φgrad(u) + u × grad(φ)

Correct : a

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