If the lines `(x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1` intersect then the value of k is (A) `3/2` (B) `9/2` (C) `-2/9` (D) `-3/2`

Options

A. `3//2`
B. `9//2`
C. `-2//9`
D. `-3//2`

Answer

b

Explanation

`(x-1)/(2)= (y+1)/(3)= (z-1)/(4)=lamda`
`rArr" "x=2lamda+1, y=3lamda-1 and z=4lamda+1`
`" "(x-3)/(1)= (y-k)/(2)= (z)/(1)= mu`
`rArr" "x=3+mu, y=k+2mu and z=mu `
Since the above lines intersect,
`" "2lamda+1= 3+mu" " `(i)
`" "3lamda-1= 2mu +k" "` (ii)
`" "mu = 4lamda +1" "` (iii)
Solving (i) and (iii) and putting the value of `lamda and mu` in (ii), `k = 9//2`.