should the diagram say u and v instead of u^ and v^?

yzliu567

It should be u hat and v hat because they represent a 2d vector (a direction on the 2d plane)

akshitdewan

ah, whereas u and v are points?

yzliu567

Normally u and v (or any letter without a hat or bold) represent scalars.

Staffjamesfobrien

A hat on a vector often (not always) indicates that the vector is a normalized vector of unit length so that v=v/|v|. (Different from a homogenized vector with w=1.)

The axes of an orthonormal coordinate system should be of unit length. That is why you will often see a hat on the labels of coordinate frame.

should the diagram say u and v instead of u^ and v^?

It should be u hat and v hat because they represent a 2d vector (a direction on the 2d plane)

ah, whereas u and v are points?

Normally u and v (or any letter without a hat or bold) represent scalars.

A hat on a vector often (not always) indicates that the vector is a normalized vector of unit length so that v=v/|v|. (Different from a homogenized vector with w=1.)

The axes of an orthonormal coordinate system should be of unit length. That is why you will often see a hat on the labels of coordinate frame.