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The lines (x-1)/1=(y+1)/-1=z/2 and x/2=(...

The lines `(x-1)/1=(y+1)/-1=z/2` and `x/2=(y-1)/-2=(z-1)/lambda` are

A

parallel if `lambda=4`

B

perpendicular if `lambda=-1`

C

coplanar if `lambda=4`

D

skew lines `lambda=5`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`L_(1):(x-1)/1=(y+1)/-1=z/2` passes through the point `A(1,-1,0)` and its parallel to vectors `vecn_(1)=hati+hatj+2hatk`
`L_(2):x/2=(y-1)/-2=(z-1)/lambda` passes through the point B(0,1,1) and it is parallel to vectors `vecn_(2)=2hati-2hatj+lambdahatk`.
a) If lines are perpendicular then `vecn_(1).vecn_(2)=0`
`therefore 2+2+2lambda=0 rArr lambda=-2`
b) If lines are perpendicular then `vecn_(1).vecn_(2)=0`
`therefore 2+2+2lambda=0 rArr lambda=-2`
c) Clearly, for `lambda=4`, lines are parallel and hence thay are coplanar.
Coplanar for `lambda=4`.
d) For `lambda=5, vec(AB).(vecn_(1) xx vecn_(2)) ne =0`
Hence, lines are skew.
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