jee-main 2022 Q79

jee-main · India · session2_28jul_shift2 Vectors: Lines & Planes Volume of Pyramid/Tetrahedron Using Planes and Lines

A plane $P$ is parallel to two lines whose direction ratios are $- 2,1 , - 3$ and $- 1,2 , - 2$ and it contains the point $( 2,2 , - 2 )$. Let $P$ intersect the co-ordinate axes at the points $A , B , C$ making the intercepts $\alpha , \beta , \gamma$. If $V$ is the volume of the tetrahedron $O A B C$, where $O$ is the origin and $p = \alpha + \beta + \gamma$, then the ordered pair $( V , p )$ is equal to
(1) $( 48 , - 13 )$
(2) $( 24 , - 13 )$
(3) $( 48,11 )$
(4) $( 24 , - 5 )$

A plane $P$ is parallel to two lines whose direction ratios are $- 2,1 , - 3$ and $- 1,2 , - 2$ and it contains the point $( 2,2 , - 2 )$. Let $P$ intersect the co-ordinate axes at the points $A , B , C$ making the intercepts $\alpha , \beta , \gamma$. If $V$ is the volume of the tetrahedron $O A B C$, where $O$ is the origin and $p = \alpha + \beta + \gamma$, then the ordered pair $( V , p )$ is equal to\\
(1) $( 48 , - 13 )$\\
(2) $( 24 , - 13 )$\\
(3) $( 48,11 )$\\
(4) $( 24 , - 5 )$

Paper Questions

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