csat-suneung 2013 Q25

csat-suneung · South-Korea · csat__math-science Vectors Introduction & 2D Optimization of a Vector Expression
In an equilateral triangle ABC with side length 2, let H be the foot of the perpendicular from vertex A to side BC. When point P moves on line segment AH, find the maximum value of $| \overrightarrow { \mathrm { PA } } \cdot \overrightarrow { \mathrm { PB } } |$, which is $\frac { q } { p }$. Find the value of $p + q$. (Given that $p$ and $q$ are coprime natural numbers.) 
In an equilateral triangle ABC with side length 2, let H be the foot of the perpendicular from vertex A to side BC. When point P moves on line segment AH, find the maximum value of $| \overrightarrow { \mathrm { PA } } \cdot \overrightarrow { \mathrm { PB } } |$, which is $\frac { q } { p }$.\\
Find the value of $p + q$. (Given that $p$ and $q$ are coprime natural numbers.)
Paper Questions
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