4.3.2 Subtraction of Vectors


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

Example 1:

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

Solution:
(a)
P R = P O + O R = O P + O R = p ˜ + r ˜

(b)
O Q = O P + P Q = O P + 2 5 P R = p ˜ + 2 5 ( p ˜ + r ˜ ) = p ˜ 2 5 p ˜ + 2 5 r ˜ = 3 5 p ˜ + 2 5 r ˜

(c)
Q M = Q O + O M = O Q + O M = O Q + 1 2 O R = ( 3 5 p ˜ + 2 5 r ˜ ) + 1 2 r ˜ = 3 5 p ˜ 2 5 r ˜ + 1 2 r ˜ = 3 5 p ˜ + 1 10 r ˜

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