6. How is $$ \overline{P Q} $$ different from $$ \stackrel{\rightharpoonup}{P Q} $$

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The notation $$ \overline{PQ} $$ and $$ \stackrel{\rightharpoonup}{PQ} $$ represent different concepts in geometry and vector mathematics.

1. **$$ \overline{PQ} $$**:
   - This notation typically represents a line segment between points $$ P $$ and $$ Q $$.
   - It indicates that the segment has a definite length and connects the two points directly.
   - The line segment includes both endpoints $$ P $$ and $$ Q $$.

2. **$$ \stackrel{\rightharpoonup}{PQ} $$**:
   - This notation represents a vector from point $$ P $$ to point $$ Q $$.
   - It indicates direction and magnitude but does not include the endpoints as part of the vector itself.
   - The vector $$ \stackrel{\rightharpoonup}{PQ} $$ has a specific direction pointing from $$ P $$ to $$ Q $$ and can be represented in terms of its components or coordinates.

In summary, $$ \overline{PQ} $$ refers to the physical segment connecting two points, while $$ \stackrel{\rightharpoonup}{PQ} $$ refers to the directed quantity (vector) that describes the movement from point $$ P $$ to point $$ Q $$.
$$ \overline{PQ} $$ is a line segment connecting points P and Q, while $$ \stackrel{\rightharpoonup}{PQ} $$ is a vector from P to Q.

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