Friday, 8 August 2014
CHAPTER 5 - Worked Out Examples – 2
Suppose that the vectors
represent two adjacent sides of a regular hexagon. Find the vectors representing the other sides.
Let the hexagon be
, as shown:
First of all, we note an important geometrical property of a regular hexagon:
, we have
Now we use the triangle law to determine the various sides:
(only the sense differs; support is parallel to the support of
Thus, all sides are expressible in terms of
What can be interpreted about
if they satisfy the relation:
co-initial so that they form the adjacent sides of a parallelogram:
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
form the adjacent sides of a rectangle. In other words,
are perpendicular to each other.
August 08, 2014
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#Transformation of Complex Functions : Mapping of Z plane in to W plane ...