Q: Do two intersecting lines determine a plane?

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Yes.

Intersecting lines are two lines that cross in a coordinate plane. So, yes, intersecting lines cross.

Yes. They're in the plane defined by the two intersecting lines.

The locus in a plane is two more intersecting lines, perpendicular to each other (and of course half-way between the given lines.

Yes. The two lines define a plane which they both belong to.

Related questions

Yes.

Intersecting lines are two lines that cross in a coordinate plane. So, yes, intersecting lines cross.

Yes. They're in the plane defined by the two intersecting lines.

If they are straight lines, then they define a plane in which both lines lie.

The locus in a plane is two more intersecting lines, perpendicular to each other (and of course half-way between the given lines.

Lines in a plane can intersect at only one point.

Yes. The two lines define a plane which they both belong to.

2

Two lines that are not parallel and do not intersect are skew. If the non-intersecting lines are in the same plane then they are parallel.

Lines intersect if the meet at one point. Perpendicular lines also meet at one point, but their intersection is a right angle. Intersecting lines in the plane do not meet at two points.

No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.

Orthogonal. The lines form right angles in a 2-d plane.