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Show that vecV = 3y^4z^2hati + 4x^3z^2 h...

Show that `vecV = 3y^4z^2hati + 4x^3z^2 hatj - 3x^2 y^2 hatk` is a solenoidal vector.

Text Solution

Verified by Experts

A vector is a solenoidal vector if divergence of a that vector is `0`.
`grad*(vecv) = 0`
Here, `vecv = 3y^4z^2hati+4x^3z^2hatj-3x^2y^2hatk`
`=>grad*vecv = del/(delx)(3y^4z^2)+del/(dely)(4x^3z^2)-del/(delz)(3x^2y^2)`
`=0+0-0 = 0`
Hence, given vector is a solenoidal vector.
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