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1
(MMP) Problem No. 21
Solution
2
3
4
1 2 3
1 2
2 3
(1,1,1), (2,3,4), (3,0, 1)
(2 1) (3 1) (4 1)
2 3
(3 2) (0 3) ( 1 4)
3 5
P P P
i J k
i j k
i J k
i j k

     
  
      
  
P P
P P
5
1 2 2 3
2 3
4
,
1 2 3
1 3 5
( 1) ( 10 9) ( 1) ( 5 3)
( 1) ( 3 2) 8 5
Now
i j k
X
i X j X
k X i j k

 
        
      
P P P P
6
1 2 2 3 8 5
1 64 25 90 3 10
1 3
3 10 10
2 2
and
X i j k
A X
   
    
  
P P P P

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Area of a Triangle.doc

  • 1. 1 (MMP) Problem No. 21 Solution
  • 2. 2
  • 3. 3
  • 4. 4 1 2 3 1 2 2 3 (1,1,1), (2,3,4), (3,0, 1) (2 1) (3 1) (4 1) 2 3 (3 2) (0 3) ( 1 4) 3 5 P P P i J k i j k i J k i j k                     P P P P
  • 5. 5 1 2 2 3 2 3 4 , 1 2 3 1 3 5 ( 1) ( 10 9) ( 1) ( 5 3) ( 1) ( 3 2) 8 5 Now i j k X i X j X k X i j k                    P P P P
  • 6. 6 1 2 2 3 8 5 1 64 25 90 3 10 1 3 3 10 10 2 2 and X i j k A X             P P P P