Page 273 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

3. Calculate the length of the following vectors.
(a) AB =(-5 ) (b) PQ =(-7) 4 -8
(c) KL = ( 3 ) (d) XY =( 6 ) 6 -9
4. Calculate the magnitude of the following vectors.
(a) AB =( 8 ) (b) PQ =( -9 ) 24
POSITION VECTOR
(a) AB = ( ) 14
(b) PQ =( ) 15
Find OA in the form( xy ) (ii) Calculate the magnitude of OA.
(c) KL =(
14 -15
-17
10
-13
)
(d) XY =( ) -15
y
267
GIVEN A POINT
y
y
0 (0,0)
(i)
O (0, 0 ) is the start point and A (7 , 4) is the end point of OA.
P(x,y)
x
x
(c) KL =(-7) -8
5. Calculate the size of the
(a) AB =(-9 ) 11
(d) XY =( 9 ) -10
following vectors.
(b) PQ =(10) -15
A position vector always starts from the origin O (0, 0).
In the diagram OP is a position vector.
If P is the point (x, y), then the position vector, O P = ( xy )
EXAMPLE 4
(c) KL =(
12 10
)
(d) XY =( ) -13
represented by the
6. Calculate the distance following vectors.
(a)
(a)
4
0
-10
(i) The position vector, OA = ( 74 ) The magnitude of OA, OA = √72 + 42
= √(49+16) = √65
= 8.06 units
P(x,y) 4
x
(correct to 3 s.f.)
7
OP
OA = 8.06 units O A = ( 74 )