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Coordinate System

For the transformation
[itex]u_1=2x-y[/itex]
[itex]u_2=x+2y[/itex]
[itex]u_3=3z[/itex]

verify that the [itex]u_i[/itex] form an orthogonal curvilinear coordinate system
 

lanedance

Homework Helper
3,304
2
any ideas? how do you show ui & uj are orthogonal when j does not equal i
 
show dot product is 0.
if [itex]u_1=(2x,-y,0),u_2=(x,2y,0)[/itex] then
[itex]u_1 \cdot u_2 = 2x^2 -2y^2 \neq 0[/itex] though
 

gabbagabbahey

Homework Helper
Gold Member
5,001
6
Are you sure that the vectors aren't supposed to be:
[tex]\vec{u_1}=2\hat{x}-\hat{y}[/tex]
[tex]\vec{u_2}=\hat{x}+2\hat{y}[/tex]
[tex]\vec{u_2}=3\hat{z}[/tex]

.....there is a big difference between the scalar [itex]x[/itex] and the unit vector [tex]\hat{x}[/tex]!:wink:
 

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