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As I understand, the normalize setting should convert a vector into a unit vector. However, I am confused as two what the second vector input does in this operation. Normalizing should only require one vector input right?

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For the normalize option the node will only normalize the first input vector (set the length to 1). You are right, a second vector isn't needed for this operation.

This example shows how it can be used to multiply a vector by a scalar:

enter image description here

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    $\begingroup$ I recently encountered another instance of this with Cycles nodes where only one of the inputs is actually used. I think this was done to avoid the extra code needed for lots of different node configurations. It is confusing. $\endgroup$ – MarcClintDion Nov 15 '14 at 18:56

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