Question

1. a) Determine whether the following force field F is conservative:
F = xi-y +zk​

Answer 1

xi-yj +zk is a conservative vector feild

•F = xi-yj +zk

•let F is in the form of ai + bj + ck

then , for conservative vector feild

del × F = 0

•i.e. | i j k |

| d/dx d/dy d/dz | = 0

| a b c |

•This means for F to be conservative

| i j k |

| d/dx d/dy d/dz | = 0

| x -y z |

i( dz/dy + dy/dz ) -j( dz/dx - dx/dz)

+ k ( -dy/dx - dx/dy)

= i( 0+0) -j(0-0) + k(0-0) = 0

•Hence F is conservative