Vectors and Triangles

This item is taken from IGCSE Mathematics (0580) Paper 41 of October/November 2010.


To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Vectors
   (b) Specific topic: Addition and Subtraction of Vectors
   (c) Concept needed:

To answer (i), let us use the given statement and name vector QT in terms of t.

To answer (ii), let us also use the given then determine the relation of the sides.

Let us take note that vector OT and OR starts at the same vertex. This suggest that the resultant is the difference of these two vectors. That is

To answer (iii), let us use the answers from (i) and (ii), and the triangle that they formed.

Therefore,

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