Let L1: x-13= y-1-1= z+10 and L2: x-22= y0= z+4 , , 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 .
216
Equating points of L1 and L2: B=(4,0,-1) and =3. A(1,1,-1) lies on L1 (at t=0), so PB is the projection of AB on L2.
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AB=(3,-1,0), d=(2,0,3): PB= | AB d|| d|= 6 13
26 (PB)2=26 3 3613=216
Answer: 216
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