# Answer to Question #37613 in Geometry for amal

Question #37613

Hi

Recall that we can thought of a projective plane as an upper hemisphere. We define the binary operation on a projective plane as follows: Let x and y be any two points belong to the projective plane, think of the projective plane as an upper hemisphere. Then take the antipodal point of y which is in the lower hemispher and identified with y. Draw a line through x and the antipodal point of y. Then draw a line parallel to that line with same length and the origin is the mid point, x*y is then defined as the endpoint of this line (Since the end points are antipodal so they are equal in RP).

My question is

Is it true that x*(y*z)=(x*y)*(x*z) for x,y,z in RP

If yes, then can you prove it for me please

thank you in advance

Recall that we can thought of a projective plane as an upper hemisphere. We define the binary operation on a projective plane as follows: Let x and y be any two points belong to the projective plane, think of the projective plane as an upper hemisphere. Then take the antipodal point of y which is in the lower hemispher and identified with y. Draw a line through x and the antipodal point of y. Then draw a line parallel to that line with same length and the origin is the mid point, x*y is then defined as the endpoint of this line (Since the end points are antipodal so they are equal in RP).

My question is

Is it true that x*(y*z)=(x*y)*(x*z) for x,y,z in RP

If yes, then can you prove it for me please

thank you in advance

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## Comments

Assignment Expert25.12.13, 14:44Dear amal

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amal24.12.13, 21:56Thank you so much. You answered my question perfectly. thaaaaaaaaaank you

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