If $C$ is the midpoint of $A B$ and $P$ is any point outside $A B$ , then $- - \to P A + - - \to P B =$

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Solution

$- - \to P A = - - \to P C + - - \to C A$
$- - \to P B = - - \to P C + - - \to C B$
$- - \to P A + - - \to P B = 2 - - \to P C + (- - \to C A + - - \to C B)$
$= 2 - - \to P C$ $(∵ - - \to C A = - - - \to C B)$
Hence $- - \to C A + - - \to C B = 0$
and $- - \to P A + - - \to P B = 2 - - \to P C$

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