Coordinate System

latentcorpse

For the transformation
$u_1=2x-y$
$u_2=x+2y$
$u_3=3z$

verify that the $u_i$ form an orthogonal curvilinear coordinate system

Related Advanced Physics Homework Help News on Phys.org

lanedance

Homework Helper
any ideas? how do you show ui & uj are orthogonal when j does not equal i

latentcorpse

show dot product is 0.
if $u_1=(2x,-y,0),u_2=(x,2y,0)$ then
$u_1 \cdot u_2 = 2x^2 -2y^2 \neq 0$ though

gabbagabbahey

Homework Helper
Gold Member
Are you sure that the vectors aren't supposed to be:
$$\vec{u_1}=2\hat{x}-\hat{y}$$
$$\vec{u_2}=\hat{x}+2\hat{y}$$
$$\vec{u_2}=3\hat{z}$$

.....there is a big difference between the scalar $x$ and the unit vector $$\hat{x}$$!

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving