Problems in Mathematical Analysis · 8.17

Find the flux of the vector $\overrightarrow {a}=y\overrightarrow {i}+z\overrightarrow {j}+x\overrightarrow {k}$ through the entire surface of the pyramid bounded by the planes $x=0$, $y=0$, $z=0$, $x+y+z=a$ $(a>0)$.

Verify the result using the Ostrogradsky formula.