Question

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.

Answer 1

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`