If line `(2x-4)/(lamda)=(lamda-1)/(2)=(z-3)/(1) and (x-1)/(1)=(3y-1)/(lamda)=(z-2)/(1)`
are perpendicular to each then `lamda=` . . .

Options

A. 7
B. `-(7)/(6)`
C. `6`
D. `-(6)/(7)`

Answer

D

Explanation

Given lines are `(2x-4)/(lamda)=(y-1)/(2)=(z-3)/(1)`
`implies(x-2)/((lamda)/(2))=(y-1)/(2)=(z-3)/(1)` . . . (i)
and `(x-1)/(1)=(3y-1)/(lamda)=(z-2)/(1)`
`implies(x-1)/(1)=(y-(1)/(3))/((lamda)/(3))=(z-2)/(1)` . . . (ii)
Since, lines (i) and (ii) are perpendicular
`therefore(lamda)/(2)xx1+2xx(lamda)/(3)+1xx1=0`
`implies(lamda)/(2)+(2lamda)/(3)+1=0`
`implies3lamda+4lamda+6=0`
`implies7lamda=-6`
`implieslamda=-(6)/(7)`