taiwan-gsat 2023 Q16

taiwan-gsat · Other · gsat__math-a 5 marks Vectors: Lines & Planes Perpendicular/Orthogonal Projection onto a Plane

Let $E: x + z = 2$ be the plane in coordinate space passing through the three points $A(2,-1,0)$, $B(0,1,2)$, $C(-2,1,4)$. There is another point $P$ on the plane $z = 1$ whose projection onto $E$ is equidistant from points $A$, $B$, and $C$. Then the distance from point $P$ to plane $E$ is (16--1)$\sqrt{16\text{-}2}$. (Express as a simplified radical)

Let $E: x + z = 2$ be the plane in coordinate space passing through the three points $A(2,-1,0)$, $B(0,1,2)$, $C(-2,1,4)$. There is another point $P$ on the plane $z = 1$ whose projection onto $E$ is equidistant from points $A$, $B$, and $C$. Then the distance from point $P$ to plane $E$ is (16--1)$\sqrt{16\text{-}2}$. (Express as a simplified radical)

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