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JEE Main202522 Jan 2025Morning ShiftMathematicsThree Dimensional GeometryActual

Let L ₁: x-1 3 = y-1 -1 = z+1 0 and L ₂: x-2 2 = y 0 = z+4 , R , be two lines, which intersect at the point B . If P is the foot of perpendicular from the point A(1,1,-1) on L₂ , then the value of 26 ( ~PB )^2 is _________

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Step-by-step solution

Point B aligned & (3 +1,- +1,-1) (2 +2,0, -4) & 3 +1=2 +2 & - +1=0 & -1= -4 & =1, =1, =3 & B(4,0,-1) aligned Let Point ' P ' is (2 +2,0,3 -4) Dr's of AP A P L₂ = 7 13 P ( 40 13 , 0, -31 13 ) 26 (P B)^2=26 3 ( 144 169 + 324 169 )=216

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