1.18 Given: A = z²yi + (x - y)k, B = zi, and = xy³z³. Find (a) div B, (b) (c) grad d. 1.19 If = 0, show that Vo is both solenoidal and irrotational. 1.20 If A is irrotational, show that Axr is solenoidal. 1.21 Find the directional derivative of p(x, y, z) = 2x³ - 3yz at the point (2,1,3) in the direction parallel to the vector with components given by (2,1,-2). 1.22 Find a unit normal to the surface = 2 + yz = C at the point (2, 1, 1). 1.23 Compute the line integral along the line segment joining (0,0,0) and (1,2,4) if A = r²i+yj + (xz - y)k. 1.24 By use of Maxwell's equations for a vacuum, show that V2E = 60/40 8² Ex at² Curl A, and > V² Ey=60/40- ² Ey and V2E₂ = 60/40- " Ət² 8² E₂ at² 1.25 In Maxwell's electromagnetic theory, choose the vector and scalar potentials (A and =) such that

1.18 Given: A = z²yi + (x - y)k, B = zi, and = xy³z³. Find (a) div B, (b) (c) grad d. 1.19 If = 0, show that Vo is both solenoidal and irrotational. 1.20 If A is irrotational, show that Axr is solenoidal. 1.21 Find the directional derivative of p(x, y, z) = 2x³ - 3yz at the point (2,1,3) in the direction parallel to the vector with components given by (2,1,-2). 1.22 Find a unit normal to the surface = 2 + yz = C at the point (2, 1, 1). 1.23 Compute the line integral along the line segment joining (0,0,0) and (1,2,4) if A = r²i+yj + (xz - y)k. 1.24 By use of Maxwell's equations for a vacuum, show that V2E = 60/40 8² Ex at² Curl A, and > V² Ey=60/40- ² Ey and V2E₂ = 60/40- " Ət² 8² E₂ at² 1.25 In Maxwell's electromagnetic theory, choose the vector and scalar potentials (A and =) such that