csat-suneung 2013 Q20

csat-suneung · South-Korea · csat__math-science 4 marks Vectors 3D & Lines Volume of a 3D Solid

In coordinate space, one face ABC of a regular tetrahedron ABCD lies on the plane $2 x - y + z = 4$, and the vertex D lies on the plane $x + y + z = 3$. When the centroid of triangle ABC has coordinates $( 1,1,3 )$, what is the length of one edge of the regular tetrahedron ABCD? [4 points]
(1) $2 \sqrt { 2 }$
(2) 3
(3) $2 \sqrt { 3 }$
(4) 4
(5) $3 \sqrt { 2 }$

In coordinate space, one face ABC of a regular tetrahedron ABCD lies on the plane $2 x - y + z = 4$, and the vertex D lies on the plane $x + y + z = 3$. When the centroid of triangle ABC has coordinates $( 1,1,3 )$, what is the length of one edge of the regular tetrahedron ABCD? [4 points]\\
(1) $2 \sqrt { 2 }$\\
(2) 3\\
(3) $2 \sqrt { 3 }$\\
(4) 4\\
(5) $3 \sqrt { 2 }$

Paper Questions

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