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)
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