Line perpendicular how to determine the line and the plane is what the relationship between

Determination method:

1, a straight line out of the plane, if and the plane of the two intersecting straight line perpendicular, then, this line is perpendicular to the plane.

2, if a line is known and a plane a perpendicular, then this line and all parallel to the plane a plane perpendicular.

3. If a line l is known to be perpendicular to a plane, then all lines parallel to line l are perpendicular to that plane.

Definition of perpendicularity of a line to a plane:

A straight line out of a plane is said to be perpendicular to the plane if it is perpendicular to any line in the plane.

Extended information:

Methods of proving that a line is perpendicular to a plane: Algebraic method

As in the figure , l is perpendicular to both intersecting lines a, b in α. Prove: l ⊥ α

Proof: a line that is parallel to a or b must be perpendicular to l, so the rest of the discussion centers around lines that are not parallel to a, b.

First, a, b, l translation to intersect at point O, O for any line g, in g on the point G, G for GB ∥ a ∥ b in B, G for GA ∥ b ∥ a ∥ A in A. Connection AB, set the intersection point of AB and OG for C

∵ OA ∥ GB, OB ∥ GA

∴ Quadrilateral OAGB is a parallelogram

∴C is the midpoint of AB

By the median theorem,

Take the point D on l which is different from O, connect DA,DB, by the median theorem

The two formulas can be subtracted to get

And notice that OD ⊥ OA,OD ⊥ OB

∴Get

That is,

∴OD ⊥OC

By the arbitrariness of g It can be seen that l is perpendicular to any line in α

∴l⊥α