CHAPTER 4 GRADIENT, DIVERGENCE CURL AND QUESTIONS 1) Find the angle between the surfaces at 9 3 x  y  z  and z   y 2 2 2 2 2 (2,-1,2) the point Ans. 54 0 R A(a,b,c) P(x,y,z). 2) Let be the distance from a fixed point to any point Show that is a unit vector in the direction .  AP R 3) Prove that r3  r  r  4) Evaluate  r f Ans. 0 r  5) Evaluate f 2 2 df d f 2  2 r dr Ans. 6xy iˆ 3x ˆj 3xz kˆ 6) Show that is irrotational.     A z z y 3 2 2 7) If are A and B 54 prove that is  A B
CHAPTER 4 GRADIENT, DIVERGENCE AND CURL QUESTIONS 1) Find the angle between the surfaces x 2  y 2  z 2  9 and z  2  y 2 3 at the point (2,-1,2) Ans. 54 0 2) Let R be the distance from a fixed point A(a,b,c) to any point P(x,y,z). Show that is a unit vector in the direction AP  R . 3) Prove that  r3 r 4) Evaluate  r f r   Ans. 0 5) Evaluate 2 f r  Ans. d 2 f 2  2 df r dr 6) Show that A  6xy  z 3 iˆ  3x 2 z ˆj  3xz 2 y kˆ is irrotational. 7) If A and B are prove that A  B is 54