jee-main 2022 Q80

jee-main · India · session1_26jun_shift2 Vectors 3D & Lines MCQ: Relationship Between Two Lines
If the lines $\vec { r } = ( \hat { i } - \hat { j } + \widehat { k } ) + \lambda ( 3 \hat { j } - \widehat { k } )$ and $\vec { r } = ( \alpha \hat { i } - \hat { j } ) + \mu ( 2 \hat { i } - 3 \widehat { k } )$ are co-planar, then the distance of the plane containing these two lines from the point $( \alpha , 0,0 )$ is
(1) $\frac { 2 } { 9 }$
(2) $\frac { 2 } { 11 }$
(3) $\frac { 4 } { 11 }$
(4) 2
If the lines $\vec { r } = ( \hat { i } - \hat { j } + \widehat { k } ) + \lambda ( 3 \hat { j } - \widehat { k } )$ and $\vec { r } = ( \alpha \hat { i } - \hat { j } ) + \mu ( 2 \hat { i } - 3 \widehat { k } )$ are co-planar, then the distance of the plane containing these two lines from the point $( \alpha , 0,0 )$ is\\
(1) $\frac { 2 } { 9 }$\\
(2) $\frac { 2 } { 11 }$\\
(3) $\frac { 4 } { 11 }$\\
(4) 2