Example: 2 | |
Suppose that the vectors and represent two adjacent sides of a regular hexagon. Find the vectors representing the other sides.
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Solution: 2 | |
Let the hexagon be , as shown:
First of all, we note an important geometrical property of a regular hexagon:
Also, since , we have
Now we use the triangle law to determine the various sides:
Thus, all sides are expressible in terms of and .
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Example: 3 | |
What can be interpreted about and if they satisfy the relation:
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Solution: 3 | |
Make and co-initial so that they form the adjacent sides of a parallelogram:
We have,
Thus, the stated relation implies that the two diagonals of the parallelogram are equal, which can only happen if is a rectangle.
This implies that and form the adjacent sides of a rectangle. In other words, and are perpendicular to each other.
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