Find curl F for the vector field at the given point. F(x, y, z) = x2zi − 2xzj + yzk; (7, −9, 3)?

I'm missing something. I got 17i-14j+6k for my answer which was wrong.

1 Answer
Jul 29, 2018

Answer:

The curl is #=21veci+49vecj-14veck#

Explanation:

#F(x,y,z)=x^2zveci-2xzvecj+yzveck#

The curl of a vector field is defined as

#curl F=nabla xxF#

#=|(veci, vecj,veck),(del/(delx),del/(dely), del/(delz)),(x^2z,-2xz,yz)|#

#=veci|(del/(dely), del/(delz)),(-2xz,yz)|-vecj|(del/(delx),del/(delz)),(x^2z,yz)|+veck|(del/(delx),del/(dely)),(x^2z,-2xz)|#

#=veci(z+2x) -vecj(0-x^2)+veck(-2z-0)#

#=veci(z+2x)+vecjx^2-veck2z#

At the point #(7,-9,7)#, the curl is

#=veci21+vecj49-veck14#