GATE Civil Engineering (CE) 2023 Shift 2 Solved Paper

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Question : 11 of 65

Marks: +1, -0

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

div(𝜙𝒖) = 𝜙div(𝒖) + 𝒖 ⋅ grad(𝜙)
div(𝜙𝒖) = 𝜙div(𝒖) + 𝒖 × grad(𝜙)
div(𝜙𝒖) = 𝜙grad(𝒖) + 𝒖 ⋅ grad(𝜙)
div(𝜙𝒖) = 𝜙grad(𝒖) + 𝒖 × grad(𝜙)

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