Mathematics (vector calculus) nle : if (xyz)" (x°i+y"j+z"k) is a irrotational vector, then prove that either b = 0 ora= -1. example: if solution. let f be the g

Mathematics (Vector Calculus) nle : If (xyz)" (x°i+y"J+z"k) is a irrotational vector, then prove that either b = 0 ora= -1. Example: If Solution. Let f be the given vector, then k curl f =V x f= Ox oy Oz x (xyz y' (xyz z' (xyz" -B xyz y = Ei bxyb-ab bxyabb-1 = b(xyz) i(za y1- y" z') boxyz) za1- y yz ya-- xa +k ,a+1 xa-za+1 = b(xyz) Xy ZX yz curl f = 0 NOW f is irrotational vector which is possible, when ya+1 = 0 = xa*1- za*1 = ya*1-xa*1 b(xyz)= 0 or, za*1- y = 0 = x a =-1 L.e. whenb 0 or, a+ 1 = 0 it zk and a is any constant vector; then prove that .I didn't understand the 4th step.

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