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JEE Main20258 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

Let the area of the triangle formed by the lines x+2=y-1=z, x-3 5 = y -1 = z-1 1 and x -3 = y-3 3 = z-2 1 be A . Then A^2 is equal to ________

Correct answer

0

Step-by-step solution

aligned & L ₁: x +2= y -1= z = & L ₂: x -3 5 = y -1 = z -1 1 = m & ~L ₃: x -3 = y -3 5 = z -2 1 = n aligned Point of intersection of L₁ and L₂ . array r -2=5 ~m +3 +1=- m = m +1 array =0, ~m =-1 ~A (-2,1,0) Point of intersection of L₂ and L₃ . array l 5 ~m +3=-3 n - m =3 n +3 ~m +1= n +2 array m =0, n =-1, B(3,0,1) Point of intersection L₃ and L₄ . array r -3 n = -2 3 n +3= +1 n +2= array =2, n =0, C (0,3,2) aligned & Ar ( ABC )= | 1 2 | array ccc i & j & k -5 & 1 & -1 -3 & 3 & 1 array | | & A = 1 2 | i (4)- j (-8)

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