Question

A line `L_(1)` with direction ratios `-3,2,4` passes through the point A(7,6,2) and a line `L_(2)` with directions ratios 2,1,3 passes through the point B(5,3,4). A line `L_(3)` with direction ratios `2,-2,-1` intersects `L_(1)` and `L_(3)` at C and D, resectively.
The lenth CD is equal to
A. 4
B. 6
C. 9
D. 11

Answer 1

Correct Answer - C
`L_(1) = (x-7)/-3= (y-6)/2 = (z-2)/4` and `L_(2) = (x-5)/2=(y-3)/1=(z-4)/3`
`therefore D(2mu+5,mu+3,3mu+4)`
So, `(2-3lambda-2mu)/2=(3+2lambda-mu)/-2=(-2+4lambda-3mu)/-1`
`therefore lambda=2, mu=1`
So, C(1,10,10) and D(7,4,7) `rArr` CD=9.