6. If f = x + y +2- 8, then find gradf at (2,0,2). 7. Define...

Transcribed Image Text:

6. If f = x² + y² +2²- 8, then find gradf at (2,0,2). 7. Define solenoidal vector and irrotational vector 8. If V= (x+ 3y)i+ (y- 2z)j + (x+1 z)k is solenoidal, find 7. 9. For what value of is the vector solenoidal. 10. Find a,b,c so that the vector F = (x+2y+az)i + (bx-3y-z)j +(4x+cy+2z)k is irrotational. 11. Is the vector xi + 2yj+ 3zk, Irrotational? 12. Show that F = (x²7+ y²j+z²)k is a conservative vector field. 6. If f = x² + y² +2²- 8, then find gradf at (2,0,2). 7. Define solenoidal vector and irrotational vector 8. If V= (x+ 3y)i+ (y- 2z)j + (x+1 z)k is solenoidal, find 7. 9. For what value of is the vector solenoidal. 10. Find a,b,c so that the vector F = (x+2y+az)i + (bx-3y-z)j +(4x+cy+2z)k is irrotational. 11. Is the vector xi + 2yj+ 3zk, Irrotational? 12. Show that F = (x²7+ y²j+z²)k is a conservative vector field.