1.

Let L_(1): (x-5)/3 = (y-7)/-1 = (z+2)/1 L_(2) : (x-3)/3 = (y-3)/2 = (z-6)/4 be two lines in space. If L_(3) is a line with direction ratios lt 2, 7,-5 gt meets L_(1) and L_(2) at A and B respectively, then the value of (AB)^(2)is

Answer»

Solution :
`A(5+ 3lambda, 7-lambda, -2 + lambda)`
`B(3+ 3mu, 3 + 2mu, 6 + 4mu)`
DIRECTION of
`AB =LT 2 + 3lambda - 3mu, 4- lambda-2mu, -8 + lambda - 4mu gt`
AB is PERPENDICULAR to `L_(2)`
`11 lambda - 29 mu - 18=0`........(1)
Also `(2+3lambda - 3mu)/2 = (4- lambda - 2mu)/7 = (-8 + lambda - 4mu)/-5`
`rArr lambda + m +2=0`.........(2)
from (1) and (2) `lambda=-1`
`mu=-1`
`rArr A(2,8,-3)`and `B(0,1,2)`
`(AB)^(2) = 4+49 + 25 = 78`


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