csat-suneung 2016 Q19

csat-suneung · South-Korea · csat__math-B 4 marks Vectors 3D & Lines Dihedral Angle Computation

In coordinate space, there are a point $\mathrm { A } ( 2,2,1 )$ and a plane $\alpha : x + 2 y + 2 z - 14 = 0$. When point P on plane $\alpha$ satisfies $\overline { \mathrm { AP } } \leq 3$, what is the area of the projection of the figure traced by point P onto the $xy$-plane? [4 points]
(1) $\frac { 14 } { 3 } \pi$
(2) $\frac { 13 } { 3 } \pi$
(3) $4 \pi$
(4) $\frac { 11 } { 3 } \pi$
(5) $\frac { 10 } { 3 } \pi$

In coordinate space, there are a point $\mathrm { A } ( 2,2,1 )$ and a plane $\alpha : x + 2 y + 2 z - 14 = 0$. When point P on plane $\alpha$ satisfies $\overline { \mathrm { AP } } \leq 3$, what is the area of the projection of the figure traced by point P onto the $xy$-plane? [4 points]\\
(1) $\frac { 14 } { 3 } \pi$\\
(2) $\frac { 13 } { 3 } \pi$\\
(3) $4 \pi$\\
(4) $\frac { 11 } { 3 } \pi$\\
(5) $\frac { 10 } { 3 } \pi$

Paper Questions

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