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If the lines (x-2)/(1)=(y-3)/(1)=(z-4)/(...

If the lines `(x-2)/(1)=(y-3)/(1)=(z-4)/(lamda)` and `(x-1)/(lamda)=(y-4)/(2)=(z-5)/(1)` intersect then

A

`lamda=-1`

B

`lamda=2`

C

`lamda=-3`

D

`lamda=0`

Text Solution

Verified by Experts

The correct Answer is:
A, D
The two lines will intersect only if the shortest distance between them is zero.
`implies(veca_(2)-veca_(1)).(vecb_(1)xxvecb_(2))=0`
`|{:(1,-1,-1),(1,2,lamda),(lamda,2,1):}|=0`
`implies(1-2lamda)+(1-lamda^(2))-1(2-lamda)=0`
`implies-lamda^(2)-lamda=0`
`implieslamda=0` or `lamda=-1`
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