Question

How can 2D geometry get the same results as the vector method?

Answer 1

it is very simple that in 2 D geometry the sides are used only two

so same as the vectors also have two sides been used

once two vectors are sides are used

the resultant vectors magnitude is ( a² + b² )^1/2

and angle is tan^-1 ( b/a )

and

in 2 D geometry is also same ( a² + b² )^1/2

and angle is tan^-1 ( b/a )

so these results says that the 2D geometry get the same results as the vector method.