Problem:(adsbygoogle = window.adsbygoogle || []).push({});

Let [tex]\vec{x}[/tex] and [tex]\vec{y}[/tex] be vectors inRand define^{n}

[tex]p = \frac{x^Ty}{y^Ty}y[/tex]

and

[tex]z = x - p[/tex]

(a) Show that [tex]\vec{p}\bot\vec{z}[/tex]. Thus [tex]\vec{p}[/tex] is thevector projectionof x onto y; that is [tex]\vec{x} = \vec{p} + \vec{z}[/tex], where [tex]\vec{p}[/tex] and [tex]\vec{z}[/tex] are orthogonal components of [tex]\vec{x}[/tex], and [tex]\vec{p}[/tex] is a scalar multiple of [tex]\vec{y}[/tex]

(b) If [tex]||\vec{p}|| = 6[/tex] and [tex]||\vec{z}|| = 8[/tex], determine the value of [tex]||\vec{x}||[/tex]

My problem:

I understand the question, but have no idea how to approach it. Hints?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Vector projection problem

**Physics Forums | Science Articles, Homework Help, Discussion**