A given plane and a given line don't necessarily have to intersect at all.
If the line is parallel to the plane, then they never do.
The line can also be in the plane, and then every point on the line is also
a point in the plane.
The most likely case, though, is that the line is not parallel to the plane and
not in it. In that case, their intersection is a single point.
So I guess the best answer from the allowed choices is 'sometimes'.
Always for it to be a complete triangle with three altitudes it would have to intersect at a vertex.
Sometimes
never
Parallel lines never intersect
It depends on how you define "ways" and how you define "lines" and how you define "intersect" and what kind of geometry you're talking about, but in Euclidean geometry, lines either never intersect, or they intersect at a single point, or they can intersect at all points within the lines.
Perpendicular lines always intersect and make 90 degree angles. Parallel lines never intersect with each other.
A line and a plane that do not intersect are always skew. Skew refers to two or more lines or planes that are not parallel and do not intersect. Since a line and a plane are different-dimensional objects, they will never intersect and will always be skew.
Always for it to be a complete triangle with three altitudes it would have to intersect at a vertex.
sometimes
Never.
Sometimes
always. if two lines intersect, then exactly one plane contains the lines.
The perpendicular bisectors only intersect on the triangle when it is an isosceles right triangle.
sf sf sf
Parallel lines are always the same distance from each other and never intersect.
Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.
never