- #1

VinnyCee

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**QUESTION (5.1, #30 -> Bretscher, O.)**:

Consider a subspace V of [tex]\mathbb{R}^n[/tex] and a vector [tex]\overrightarrow{x}[/tex] in [tex]\mathbb{R}^n[/tex]. Let [tex]\overrightarrow{y}\,=\,proj_v\,\overrightarrow{x}[/tex]. What is the relationship between the following quantities?

[tex]||\overrightarrow{y}||^2[/tex] and [tex]\overrightarrow{y}\,\cdot\,\overrightarrow{x}[/tex]

__My work so far__:

I only know this for sure...

[tex]||\overrightarrow{y}||\,\leq\,||\overrightarrow{x}||\,\iff\,\overrightarrow{x}\,\in\,V[/tex]

But how do I use this to relate the two quantities? Please help, thanks!