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An equilateral triangle has each side equal to a. If the co-ordinates of its vertices are (x1, y1); (x2, y2): (x3, y3) then the square of the determinant  equals:

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DSSSB TGT Maths Male Subject Concerned- 23 Sep 2018 Shift 1
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  1. None of these
  2. 4a2
  3. 3a4

Answer (Detailed Solution Below)

Option 4 :
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Detailed Solution

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Concept:

Area of equilateral triangle = ×a2

Calculation:

Given: The co-ordinates of its vertices are (x1, y1); (x2, y2): (x3, y3) then the square of the determinant 

⇒ (△ ABC ) =   = ( ) ×a2

On squaring both side, 

⇒    = 

⇒  = 

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Q1.Consider a system equation \(2x+y-z=0\), \(4x - py + 4z = 4\) and \(x-y+z=q\) where \(p, q \in I\) and \(p, q \in [1, 10]\), then identify the correct statement(s).   List-I List-II (I) Number of ordered pairs \((p, q)\) for which system of equation has unique solution is (P) 1 (II) Number of ordered pairs \((p, q)\) for which system of equation has no solution is (Q) 9 (III) Number of ordered pairs \((p, q)\) for which system of equation has infinite solution is (R) 91 (IV) Number of ordered pairs \((p, q)\) for which system of equation has atleast one solution is (S) 90
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Q1.If P is a skew-symmetric matrix of order 3, then what is det(P) equal to? 
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