Scalar(dot product) of two vectors and some real number t.

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I was wondering if this is correct:

"The dot product of two vectors, where vector u gets multiplied by a real number t."

(t$\vec{u})\cdot\vec{v}$ = u$\cdot (t \vec{v})$, t$\in\Bbb{R}$

At first, I thought the professor just missed the arrow above u on the right side of the equation, but it said the same thing when I checked the notes. It does not feel right, but I know too little about vectors to say for sure. If this is right, how do I use u as a non-vector?