engineering recuitment GATE IN Test Series 2023-24 Mock Test Engineering Mathematics Calculus Vector Calculus
Let \(\vec u = - x\hat i + y\hat j + z\hat k\) and \(\vec v = y{z^2}\hat i + x{z^2}\hat j + 2xyz\hat k\). If \(\vec u\;and\;\vec v\) are irrotational vectors satisfying the condition \(\vec \nabla \cdot \left( {\vec u \times \vec v} \right) + f\left( {x,y,z} \right) + \vec u \cdot \vec v = 0,\) then f(x, y, z) is equal to
1
xy2z
2
–2xyz2
3
xy2 + z
4
-2xy2 + z2