Let `P`be a pointin the first octant, whose image `Q`in theplane `x+y=3`(that is,the line segment `P Q`isperpendicular to the plane `x+y=3`and themid-point of `P Q`lies in theplane `x+y=3)`lies on the z-axis. Let the distance of `P`from the x-axis be 5. If `R`is theimage of `P`in thexy-plane, then the length of `P R`is _______.

Let `P`be a pointin the first octant, whose image `Q`in theplane `x+y=

1.	Let `P`be a pointin the first octant, whose image `Q`in theplane `x+y=3`(that is,the line segment `P Q`isperpendicular to the plane `x+y=3`and themid-point of `P Q`lies in theplane `x+y=3)`lies on the z-axis. Let the distance of `P`from the x-axis be 5. If `R`is theimage of `P`in thexy-plane, then the length of `P R`is _______.
Answer» Correct Answer - 8 Let `P(alpha,beta,gamma)` and R is image of P in the xy-plane. `:.R(alpha,beta,-gamma)` Also, Q is the imgae of P in the plane `x+y=3` `:.(x-alpha)/(1)=(y-beta)/(1)=(z-gamma)/(0)=(-2(alpha+beta-3))/(2)` `x=3-beta,y=3-alpha,z=gamma` Since, Q is lies on Z-axis `:." "beta=3,alpha=3,z=gamma` `:.P(3,3,gamma)` Given, distance of P from X-axis be 5. `:." "5=sqrt(3^(2)-gamma^(2))` `25-9=gamma^(2)` `impliesgamma=+-4` Then, `" "PR=\|2gamma\|=\|2xx4\|=8`

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