# How do you rearrange equations with dot products in them?

How can I go about rearranging an equation similar to this...

$$\left(\pmatrix{-3\\0\\1}+ t \pmatrix{1\\4\\7} \right) \cdot n - a = 0$$

The issue I'm having is manipulating dot products

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That is, $$a\cdot(b+c) = a\cdot b + a\cdot c.$$
$$a(u\cdot v)=au\cdot v=u\cdot av\\ u\cdot(v+w)=(u\cdot v)+(u\cdot w)\\u\cdot v=v\cdot u\\u\cdot u> 0\:\:\mbox{if and only if }u\neq 0$$