simple dumb vector question

Question

so I've started vector calc otherwise known as calc 3

and simple question

for the image above does the vector $\parallel v \parallel$ or $\overrightarrow{PQ}$ change as the initial point moves from the origin along the $x$ axis (or $a$)? I mean does the length of the vector change, with terminal point $Q$ remaining the same, and $P$ (origin) moving along '$a$' -- I'm thinking yes because $x_1-x_0$ is now different.

Answer 1

$$\text{To elaborate on @Chris K explanation here you go}$$

$$\textbf{Q} = (a,b,c) \text{ and take } \textbf{P} = (a',0,0)$$

$$\text{Compute} \ \ \vec{PQ} = (a-a',b,c)$$

$$\text{You are traveling on the $x$-axis so $a' \neq 0$, $b=c=0$}$$

$\textbf{Conclude}$: As $a'$ changes, so does the vector.