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Vectors on Triangles (Part 1)

addition of vectors,subtraction of vectors,position vectors,naming a vector in terms of two other vectors,equal vectors,parallel vectors,triangle law for vectors
This item is taken from IGCSE Mathematics (0580) Paper 2 of October/November 2007.


To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Vectors
   (b) Specific topic: Addition/Subtraction of Vectors, Position Vectors, Naming a Vector in Terms                                 of other Two Vectors
   (c) Concepts Needed: Triangle Law for Addition/Subtraction of Vectors
addition of vectors,subtraction of vectors,position vectors,naming a vector in terms of two other vectors,equal vectors,parallel vectors,triangle law for vectors
To answer (i), take note that vector OA = a and vector OB = b. Let us divide each vector into three parts as shown:
addition of vectors,subtraction of vectors,position vectors,naming a vector in terms of two other vectors,equal vectors,parallel vectors,triangle law for vectors
Since we need 1/3 of a, we will take 1 part of a. On the other hand, we need 2/3 of b, meaning 2 parts of b.
addition of vectors,subtraction of vectors,position vectors,naming a vector in terms of two other vectors,equal vectors,parallel vectors,triangle law for vectors
Here are the vectors 1/3 a and 2/3 b:
addition of vectors,subtraction of vectors,position vectors,naming a vector in terms of two other vectors,equal vectors,parallel vectors,triangle law for vectors
Following the triangle law of addition for vectors, the end of the first vector should be the start of the second vector. This means that the the tip of 1/3 a should be the start of 2/3 b.
addition of vectors,subtraction of vectors,position vectors,naming a vector in terms of two other vectors,equal vectors,parallel vectors,triangle law for vectors
From this, we can now draw the resulting vector 1/3 a + 2/3 b. 
addition of vectors,subtraction of vectors,position vectors,naming a vector in terms of two other vectors,equal vectors,parallel vectors,triangle law for vectors
However, we are finding point C, which is the tip/end of this resulting vector.
addition of vectors,subtraction of vectors,position vectors,naming a vector in terms of two other vectors,equal vectors,parallel vectors,triangle law for vectors
Therefore, point C is located at
  
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