**Given:**

h_{14} = w_{1}x_{1}+w_{2}x_{2}+w_{3}x_{3}+w_{4}x_{4} is the dot product of the vectors

W = [w_{1}, w_{2}, w_{3}, w_{4}] and X = [x_{1}, x_{2}, x_{3}, x_{4}] written as W^{T}X.

**The neuron h_{14} will fire maximally when X = \frac{W}{||W||}:**

**If X is a unit vector defined by \frac{W}{||W||} then how is X = W same as X = \frac{W}{||W||} if magnitude of unit vector is not exactly equal to 1?**

Say for example, X = [0.4, 0.5, 0.6, 0.4] and W = [0.4, 0.5, 0.6, 0.4].

**Considering two values for X after the decimal point:**

Norm of W divided with respect to W yields X as [0.43, 0.53, 0.64, 0.43] and the magnitude results in 1.0297. Now, this is clearly greater than 1 and therefore can X be considered a unit vector here?

**Considering one value for X after the decimal point:**

Norm of W divided with respect to W yields X as [0.4, 0.5, 0.6, 0.4] and the magnitude results in 0.964. Now, in this case the magnitude is less than 1 but can 0.964 be approximated as 1 and thus can this approximation scenario be considered always? Is this the typical case a machine approximates?