In the book: Linear Algebra and its application -Gilbert Strang-, when the projection $p$ of vector $b$ onto vector $a$ is explained, this is said:
We want to find the projection point $p$. This point must be some multiple $p= \hat{x}a $ of the given vector $a$, every point on the line is a multiple of $a$.
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Why must the projection $p$ be a multiple of the vector $a$?