Question

prove that gradient of vectorA dot with vector r equals to vectorA for any constant vectorA

Answer 1

www.mas.ncl.ac.uk/~nas13/mas2104/prob4.pdf
just follow this !!

Answer 2

r(X,Y,Z) where X,Y,Z are functions of(x,y,z)
A(a,b,c)
A dot r = (aX + bY + cZ)
grad(aX + bY + cZ) =(d(aX + bY + cZ)/dx,d(aX + bY + cZ)/dy,d(aX + bY + cZ)/dz)
this is not necesarly equal A

Answer 3

if r is a position vector with coordinates r =(x,y,z) then yes.

Answer 4

gradient gives the maximum rate of change along the direction of maximum change ... the gradient of a constant vector is zero