Question of the day-0034

The divergence of the vector field \((x - y) \textbf{i} + (y - x)\textbf{j} + (x + y + z)\textbf{k}\) is

  1. 0

  2. 1

  3. 2

  4. 3

\[\overline {V}=\left( x-y\right) \overline {i}+\left( y-x\right) \overline {j}+\left( x+y+z\right) \overline {k}\] \[\nabla =\left( \dfrac {\partial }{\partial x}\overline {i}+\dfrac {\partial }{\partial y}\overline {j}+\dfrac {\partial }{\partial z}\overline {k}\right)\] \[\begin{aligned}
\nabla \cdot \overline {V} &=\dfrac {\partial }{\partial x}\left( x-y\right) +\dfrac {\partial }{\partial y}\left( y-x\right) +\dfrac {\partial }{\partial z}\left( x+y+z\right)\\
&=1+1+1 \\&=3 \end{aligned}\]

Ans: D

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