A line with direction ratio `(2,1,2)` intersects the lines `vecr=-hatj+lambda(hati+hatj+hatk)` and `vecr=-hati+mu(2hati+hatj+hatk)` at A and B, respectively then length of AB is equal to

Options

A. 1
B. 2
C. 3
D. 4

Answer

C

Explanation

`L_(1):(x-0)/1=(y+1)/1=(z-0)/1=lambda`
`L_(2):(x+1)/2=(y-0)/1=(z-0)/1=mu`
Hence any point on `L_(1)` and `L_(2)` can be `(lambda,lambda-1,lambda)` and `(2mu-1, mu, mu)` respectively.
According to the questions,
`(2mu-1-lambda)/2=(mu-lambda+1)/1=(mu-lambda)/2`
On solving, we get `mu=1` and `lambda=3`
`therefore A=(3,2,3)`and B=(1,1,1)
`therefore AB=3`