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

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.)

Explanation / Answer

basically what happens is that if there are two objects with dimensions A and B respectively , then according to the rule

if

A = B = n(say) then the resulting object has dimension n-1

A > B then resultant object has a dimension of A-B

therefore in 4 dimension if two planes intersect then

A = 4 , B = 4

therefore resultant object has dimension of 4-1 = 3 (3 dimensional plane )

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