Page 9 - 091math-wb-w1-(Vector)

WORKBOOK

Multiplication of a Vector by a Scalar:

Multiplying a vector u by a real number (scalar) k can affect the length or the direction of the
vector depending on the value of scalar.

When any vector u is multiplied with any kR the vector obtained;

a) is in the same direction, with a lesser magnitude if 0 < k < 1
b) is in the same direction, with a greater magnitude if k > 1
c) is in the opposite direction, with a lesser magnitude if -1 < k < 0
d) is in the opposite direction, with a greater magnitude if k < -1

e) is 0 if k = 0
f) is the same vector if k = 1
g) is in the opposite direction, with the same magnitude if k = -1

 
For the vectors u and v on the same plane and the real numbers k, t;

k.(u v) ku kv  
(k t).u k.u t.u  

k.(t.u) t.(k.u) (k.t).u 

   
Example 5: According to the given vectors in the figure, sketch u  v2 and v  u2 .


u


v

Negative (Opposite) Vector: Negative vectors are the vectors which have the same magnitude
but opposite directions. If opposite vector of u is denoted by -u and opposite vector of AB is
denoted by AB or BA .

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091math-wb-w1-(Vector)