taiwan-gsat 2010 Q6

taiwan-gsat · Other · gsat__math Circles Sphere and 3D Circle Problems

6. In coordinate space, $O$ is the origin and point $A$ has coordinates $(1, 2, 1)$. Let $S$ be the sphere with center $O$ and radius 4. What is the figure formed by all points $P$ on $S$ that satisfy the dot product $\overrightarrow{OA} \cdot \overrightarrow{OP} = 6$?
(1) Empty set
(2) A single point
(3) Two points
(4) A circle
(5) Two circles

& 4 & \multirow{3}{*}{C} & 18 & 4 & \multirow{2}{*}{G} & 28 & 5

6. In coordinate space, $O$ is the origin and point $A$ has coordinates $(1, 2, 1)$. Let $S$ be the sphere with center $O$ and radius 4. What is the figure formed by all points $P$ on $S$ that satisfy the dot product $\overrightarrow{OA} \cdot \overrightarrow{OP} = 6$?\\
(1) Empty set\\
(2) A single point\\
(3) Two points\\
(4) A circle\\
(5) Two circles

Paper Questions

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