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The fact is that if you have one straight line, there are an infinite number of planes in which it lies. One can see this by simply rotating the plane around the line. Thus, "a line lies in at least one plane" is a true statement.
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Does a line lie in at least one plane?
If you have one straight line, there are an infinite number of planes in which it lies.
A plane and a line intersect at a?
A point - unless the line lies within the plane, or is parallel to it.
Can two lines that coincide lie in at least one plane?
Two lines that coincide look and act exactly like a single line. If you have one straight line, there are an infinite number of planes in which it lies.
What type of intersections happen between lines and planes?
A line that does not lie within a plane and intersects the plane does so at one point.A line that lies within a plane intersects the plane at all points.
How do you find if a line lies on a point on the cartesian plane?
You first look at each axes
Does a line lie in at least one plane?
If you have one straight line, there are an infinite number of planes in which it lies.
A plane and a line intersect at a?
A point - unless the line lies within the plane, or is parallel to it.
Does a line passing through two distinct points in one plane sometimes lies in that plane?
it always lies in that plane
A line passing through two distinct points in one plane lies completely in that plane?
Always
Can two lines that coincide lie in at least one plane?
Two lines that coincide look and act exactly like a single line. If you have one straight line, there are an infinite number of planes in which it lies.
What type of intersections happen between lines and planes?
A line that does not lie within a plane and intersects the plane does so at one point.A line that lies within a plane intersects the plane at all points.
How do you find if a line lies on a point on the cartesian plane?
You first look at each axes
True or false p lies in plane b the line containing p and q must lie in plane b?
False. In order for the line PQ to lie in plane B, then both P and Q must lie in plane B.
Can a plane and a line ever intersect in two points?
In Euclidean geometry, they can only intersect in 0, 1 or infinitely many points. If there are two points of intersection then the whole line lies in the plane.
Must any lines lies in vertical plane be a vertical line?
That depends. How tough do you think it would be to draw a horizontal line or a slanting line on the wall ?
Does a plane containing 2 points of a line contains the entire line?
Yes, a plane containing 2 points of a line contains the entire line. Let us consider two points on a plane and then draw a line segment joining those two points. Since the points lie on the plane so line segment has to lie completely on that plane too. Now if we extend the line segment indefinitely in both directions we get a line and that line also has to lie on the same plane since some definite part(line segment) of it(line) also lies on the same plane.
is this statement true or falseThe steps for constructing a line perpendicular to a given line through point P are the same whether P lies on the line or not.?
false
