jee-main 2021 Q78

jee-main · India · session1_25feb_shift2 Vectors 3D & Lines Normal Vector and Plane Equation

A plane passes through the points $A ( 1,2,3 ) , B ( 2,3,1 )$ and $C ( 2,4,2 )$. If $O$ is the origin and $P$ is $( 2 , - 1,1 )$, then the projection of $\overrightarrow { O P }$ on this plane is of length:
(1) $\sqrt { \frac { 2 } { 5 } }$
(2) $\sqrt { \frac { 2 } { 7 } }$
(3) $\sqrt { \frac { 2 } { 3 } }$
(4) $\sqrt { \frac { 2 } { 11 } }$

A plane passes through the points $A ( 1,2,3 ) , B ( 2,3,1 )$ and $C ( 2,4,2 )$. If $O$ is the origin and $P$ is $( 2 , - 1,1 )$, then the projection of $\overrightarrow { O P }$ on this plane is of length:\\
(1) $\sqrt { \frac { 2 } { 5 } }$\\
(2) $\sqrt { \frac { 2 } { 7 } }$\\
(3) $\sqrt { \frac { 2 } { 3 } }$\\
(4) $\sqrt { \frac { 2 } { 11 } }$

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