Question

Find curl F for the vector field at the point (9, -9, 7). F(x,y,z) = x^2zi - 2xzj + yzk ?

Answer 1

The curl is `=25veci+81veci-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 `(9,-9,7)`, the curl is

`=veci25+veci81-veck14`