Page 285 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

From the graph: (5 ) From the graph: (4 ) (-4) a = and b = a = and b =
3 2-2
So a = b = a = - =
(5 ) (-4) (4 )
3 -22 The two vectors are equal. So a = -b
(-6)
22 2-2
length and direction.
a = b=
Two vectors that are equal can be parallel or coincident or form a straight line (or line segment).
Parallel lines are move in the same direction.
NEGATIVE VECTORS
The line segments representing a and b ; also a and c, have opposite directions but are equal in length. Each pair of lines are anti-parallel.
One vector is the negative of another vector if they have the same length but opposite direc- tions.
(-6)
(4 ) (-4)
(4 )
p = and q = a = and c =
(-6) 2
= (-4) 2
p = q = The two vectors are equal.
The line segments representing a and b ; also p and q, have the same direction and are equal in length. Each pair of lines are parallel.
Two vectors are equal if they have the same
a= - a = -c
-2
(x ) y
( yx )
Anti- parallel lines are parallel lines moving in
opposite directions.
SCALAR MULTIPLE OF A VECTOR
So
a = -b = -
279
b = ( 52 )
a = ( 42 ) -4
a =( )
-2
c =( )
-4
-2
a =( )
c =( )
10
4 -5
-2