Two general lines in a plane intersect in a point (i.e. in 2 dimensions, a 1-dim

ID: 3342702 • Letter: T

Question

Two general lines in a plane intersect in a point (i.e. in 2 dimensions, a 1-dimensional object

and a 1-dimensional object intersect in a 0-dimensional object.)

Two general planes in space intersect in a line (i.e. in 3 dimensions, a 2-dimensional object

and a 2-dimensional object intersect in a 1-dimensional object.)

A general plane and a general line in space intersect in a point (i.e. in 3 dimensions, a

2-dimensional object and a 1-dimensional object intersect in a 0-dimensional object.)

From these examples, formulate a rule for a general intersection of an object of dimension a

and an object of dimension b in n-dimensional space. In particular, what does the rule say about

intersecting two planes in 4-dimensional space? (Hint: You should think about what happens

with the codimensions; an object of dimension a in n-dimensional space has codimension n%u2212a.

Roughly, codimension counts how many directions there are to leave your object.)

for intersection the general rule is |a+b-n|

for intersection of two planes in 4-D space then a line is formed o.e. a 1 dimensional object is formed ( |3+3-4| =2 )

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