Q: Do two oblique lines determine a plane?

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plane

No.

yes they do

Yes.

Two lines with a closing of to other lines like a box

Two lines that do not intersect on the same plane are Parallel lines.

It is a 3D representation in two dimensions. Width and height are drawn on horizontal and vertical lines and depth is on an angled line, usually 30 or 45 degrees.

Two lines can lie in one plane. For example, parallel lines are lines that intersect and lie in the same plane.

two diagonal lines that aren't touching

They can be, but not necessarily. If two lines in the same plane never intersect, they are parallel. Though, two lines can exist in the same plane without being parallel. Ie, two lines that intersect at a 90 degree angle are perpendicular. Most lines in a plane aren't parallel.

Parallel lines

Yes [in the Euclidean plane].