Three lines `L_(1),L_(2),L_(3)` are given by `L_(1):vecr=lamdahati,L_(2):vecr=muhatj+hatk,L_(3):vecr=hati+hatj+gammahatk` which of the following point Q can be taken on `L_(2)` so that the point P on line `L_(1)` point Q on `L_(2)` and point R on `L_(2)` are collinear

Options

A. `hatk-(1)/(2)hatj`
B. `hatk`
C. `hatk+hatj`
D. `hatk+(1)/(2)hatj`

Answer

A, D

Explanation

`P(lamda,0,0)`
`Q(0,mu,1)`
`R(1,1,gamma)`
`vec(PQ)=kvec(PQ)implies(lamda)/(lamda-1)=(-mu)/(-1)=(-1)/(-gamma)`
`implies1+(1)/(lamda-1)=mu=(1)/(gamma)impliesmu` cannot take value of 1 and 0