- #1
msimmons
- 17
- 0
Problem:
Let [tex]\vec{x}[/tex] and [tex]\vec{y}[/tex] be vectors in Rn and define
[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 the vector projection of 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?
Let [tex]\vec{x}[/tex] and [tex]\vec{y}[/tex] be vectors in Rn and define
[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 the vector projection of 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?