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8.3.2 Subtraction of Vectors


8.3.2 Subtraction of Vectors
The subtraction of the vector b˜b˜ from the vector  a˜a˜ is written as  a˜b˜a˜b˜ . This operation can be considered as the addition of the vector a˜a˜ with the negative vector of b˜b˜ . Therefore a˜b˜=a˜+(b˜).a˜b˜=a˜+(b˜).  

Example 1:

In the diagram above, vector OP=p˜,  OR=r˜OP=p˜,  OR=r˜ and Q divides PR in the ratio of 2 : 3. Find the following vectors in terms of p˜ and r˜p˜ and r˜
(a) PR(b) OQ(c) QM if M is the midpoint of OR.

Solution:
(a)
PR=PO+OR=OP+OR=p˜+r˜

(b)
OQ=OP+PQ=OP+25PR=p˜+25(p˜+r˜)=p˜25p˜+25r˜=35p˜+25r˜

(c)
QM=QO+OM=OQ+OM=OQ+12OR=(35p˜+25r˜)+12r˜=35p˜25r˜+12r˜=35p˜+110r˜

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