Yes, you have to multiply the 1/sqrt(14) to the vector and then take the dot product of f and v. However, you should also multiply v by the reciprocal of the magnitude of v. In other words, find the normal of v.

n=1/sqrt(4^2+(-2)^2+(-1)^2) = 1/sqrt(21)

n*v =( sqrt(6)/42)(i + 3j + 2k)

Check this link with tons of examples and solutions. Go directly to page 8 and you'll see an example of your question. Also, read about DOT PRODUCT.

http://www.tech.plym.ac.uk/maths/res...X/gradient.pdf