# would we still have 90 degrees angle at B? Prob27Chap1

Discussion in 'Math' started by PG1995, Apr 16, 2012.

1. ### PG1995 Thread Starter Active Member

Apr 15, 2011
753
5
Hi

Please have a look on the attachment and kindly help me with the query there. Thanks a lot.

Regards
PG

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2. ### steveb Senior Member

Jul 3, 2008
2,433
469
Each of those angles must be 90 deg because one side is a coordinate axis and the other side is in a plane which perpendicular to that axis. The walls of the rectangle are always normal to one axis because of the way coordinates are defined in a Cartesian reference frame.

You should be able to visualize this, but if you still can't then you can prove it mathematically. The dot product of normal vectors is zero. Take the x axis and note that a vector on the x axis has the form ai where a is a constant and i is the unit vector. A vector in the wall that crosses the x axis is of the form bj+ck where b and c are constants and j and k are unit vectors for the y and z axes. Now take the dot product of these two vectors and you will see it is zero.

Last edited: Apr 16, 2012
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3. ### panic mode Senior Member

Oct 10, 2011
1,328
305
yes, OAP is right angle at A
OBP is right angle at B...

4. ### PG1995 Thread Starter Active Member

Apr 15, 2011
753
5
Thank you, Steve.

I'm sorry for belated thanks. Actually I just got free and returned to the civilization yesterday!

Best wishes
PG