Answer to Question #59580 in Calculus for RITA

Question

6 If A=xz^3i−2x^2yzj+2yz^4, find ▽×A at point (1,-1,1).
(a) 2j+3k
(b) 2i+j74k
(c) i+3j+5k
(d) 3j+4k

7 Given that A=A1i+A2j+A3k and r=xi+yj+zk , evaluate ▽⋅(A×r) if ▽×A=0
(a) 0
(b) 3
(c) 2
(d) 5

8 Let A=x^2yi−2xzj+2yzk, find Curl curl A.
(a) 3j+4k
(b) 2x+2)k
(c) (2x+2)j
(d) 3j−4k

9 Given A=2x^2i−3yzj+xz^2k and ϕ=2z−x^3y, find A⋅▽ϕ at point (1,-1,1).
(a) 5
(b) 3
(c) 4
(d) 1

10 Find the directional derivative of ϕ=x^2yz+4xz^2 at (1,-2,-1) in the direction 2i−j−2k
(a) 37/3
(b) 35/3
(c) 25/3
(d) 11/3