Friday, 8 August 2014
CHAPTER 12- Worked Out Examples – 2
Let be three non-coplanar vectors. Prove that the points
As in the previous example, we first draw a visual picture to determine when four points can be coplanar.
Thus, as explained in the figure, we must have some scalars
is the origin}
are non-coplanar, we must have
As can be easily verified, this system has the solution
are indeed coplanar.
Thus, the points
be two fixed points. Find the position vectors of the points lying on the (extended) line
which divide the segment internally and externally in the ratio
We consider internal division; the external division case follows analogously.
be the point which divides
internally in the ratio
Similarly, the point
externally in the ratio
is given by
A particular case of internal division is the mid-point of
: the mid-point is
August 08, 2014
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#Transformation of Complex Functions : Mapping of Z plane in to W plane ...