Not always. Only if the point is on the line. it
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A line intersect is a point on a line where another line or object crosses the line.
No, planes intersect at a line.
Nothing HAPPENS! They can intersect in a point or a line.
A point can be intersected by infinitely many lines. Two points intersect in only one line. Three points either intersect in a line or not at all. This is only considering two dimensions.
No, they intersect at a line.