1. alf r=xi+ yj+ zk and r= . Prove that div(rr)= (n+3)r* and curl (r F)=...

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1. alf r=xi+ yj+ zk and r= . Prove that div(r³r)= (n+3)r* and curl (r" F)= 0. blf r= xi+ yj + zk, then prove that div grad (r")= n(n+1)* ².Hence deduce that divgrad d ( ² ) = 0 2. a Find the directional derivative of p=3x²+2y-3z at (1,1,1) in the direction of 2ī +2j-k b Find the angle between the surfaces x²+y²+z²=9 and z=x²+y²-3 at the point (2,-1,2). 3. a Find the values of a and b, if the surfaces ax²-byz=(a+2)x and 4x²y+z³=4 cut orthogonally at the point (1,-1,2). b Prove that F= (y² cosx+ 2³)+ (2y sinx-4)j + 3xz²k is irrotational and find the scalar potential f. 1. alf r=xi+ yj+ zk and r= . Prove that div(r³r)= (n+3)r* and curl (r" F)= 0. blf r= xi+ yj + zk, then prove that div grad (r")= n(n+1)* ².Hence deduce that divgrad d ( ² ) = 0 2. a Find the directional derivative of p=3x²+2y-3z at (1,1,1) in the direction of 2ī +2j-k b Find the angle between the surfaces x²+y²+z²=9 and z=x²+y²-3 at the point (2,-1,2). 3. a Find the values of a and b, if the surfaces ax²-byz=(a+2)x and 4x²y+z³=4 cut orthogonally at the point (1,-1,2). b Prove that F= (y² cosx+ 2³)+ (2y sinx-4)j + 3xz²k is irrotational and find the scalar potential f.