Short Answer Type
 .
 and give a geometrical interpretation of it.
L.H.S. =Â 
       
Gemetrical Interpretation
Let O be the point of intersection of diagonals AC and BD of || gm ABCD.
      Let  
    
 implies that the area of || gm ABCD is twice the area of the || gm whose adjacent sides are semi-diagonals of the first parallelogram.
Long Answer TypeIf 
 are three vectors such that 
 show that the three vectors 
 are orthogonal in pairs and 
.
 Is the  converse true? 
 show that 
. Interpret the result 
   then prove that  
 where m is a scalar.
 and  
 then 
, where 
 is a scalar.
 and 
 then 
 are mutually perpendicular unit vectors and 
 then 
 is parallel to 
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