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A Vector field F is given by ˉF=(x2yz)ˆi+(y2zx)ˆj+(z2xy)ˆk
is irroational and hence find scalar point function ? such that F = ? ?
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Part 1:F=(x2yz)ˆi+(y2zx)ˆj+(z2xy)ˆk r=xi+yj+zkCurl F=|ˆiˆjˆkxyzx2yzy2zxz2xy|

=00+0=0F is a conservative field.there exists a scalar potential of F such that  F=φ(x2yz)ˆi+(y2zx)ˆj+(z2xy)ˆk=iφx+jφx+φx

Comparing both sides gives,φx=x2yz;φx=y2zx;φx=z2xy

Nowdφ=φxdx+φydy+φzdz dφ=(x2yz)dx+(y2zx)dy+(z2xy)dzon Integration,φ=x33yz.x+y33+z33+CScalar potential of F=φ=13(x3+y3+z3)xyz+C

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