taiwan-gsat 2025 Q14

taiwan-gsat · Other · gsat__math-a 5 marks Vectors: Lines & Planes Distance Computation (Point-to-Plane or Line-to-Line)

In coordinate space, point $A$ has coordinates $(a, b, c)$, where $a, b, c$ are all negative real numbers. Point $A$ is at distance 6 from each of the three planes $E _ { 1 } : 4 y + 3 z = 2$, $E _ { 2 } : 3 y + 4 z = - 5$, and $E _ { 3 } : x + 2 y + 2 z = - 2$. Then $a + b + c =$ (14-1) (14-2) (14-3).

In coordinate space, point $A$ has coordinates $(a, b, c)$, where $a, b, c$ are all negative real numbers. Point $A$ is at distance 6 from each of the three planes $E _ { 1 } : 4 y + 3 z = 2$, $E _ { 2 } : 3 y + 4 z = - 5$, and $E _ { 3 } : x + 2 y + 2 z = - 2$. Then $a + b + c =$ (14-1) (14-2) (14-3).

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