csat-suneung 2022 Q23 (Geometry)

csat-suneung · South-Korea · csat__math 2 marks Vectors 3D & Lines Section Division and Coordinate Computation

In coordinate space, let P be the point obtained by reflecting point $\mathrm { A } ( 2,1,3 )$ across the xy-plane, and let Q be the point obtained by reflecting point A across the yz-plane. What is the length of segment PQ? [2 points]
(1) $5 \sqrt { 2 }$
(2) $2 \sqrt { 13 }$
(3) $3 \sqrt { 6 }$
(4) $2 \sqrt { 14 }$
(5) $2 \sqrt { 15 }$

In coordinate space, let P be the point obtained by reflecting point $\mathrm { A } ( 2,1,3 )$ across the xy-plane, and let Q be the point obtained by reflecting point A across the yz-plane. What is the length of segment PQ? [2 points]\\
(1) $5 \sqrt { 2 }$\\
(2) $2 \sqrt { 13 }$\\
(3) $3 \sqrt { 6 }$\\
(4) $2 \sqrt { 14 }$\\
(5) $2 \sqrt { 15 }$

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