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prove that any two edges in a regular tetrahedron are perpendicular.

prove that any two edges in a regular tetrahedron are perpendicular.

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1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear jimmy singh


5819-1887_7662_tetra.JPG

her O is origin

OA=OB=OC=AB=BC=CA

Now AB=BC=CA

|AB|2=|BC|2=|CA|2

|b-a|2 =|c-a|2=|a-c|2

here a,b,c are position vector of A,B,C

|a|2 +|b|2 -2a.b =|b|2 +|c|2 -2c.b=|a|2 +|c|2 -2a.c


or a.b=b.c=c.a

or a.b=b.c

or  b.(a-c)=0

OB.AC=0

OB is perpendicular to AC

similerly for others


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