1. The document defines vectors and their representations, including direction, magnitude, unit vectors, and standard basis vectors. 2. Components of vectors are given with respect to the standard x, y, z coordinate axes. Position vectors locate points in space with coordinates (x,y,z). 3. Various vector operations are described such as addition, scalar multiplication, and dot and cross products. Properties of position vectors, unit vectors and applications to geometry are also covered.

1. |1
50
180 2
50
9
240
scalar
quantity
vectorquantity )
directed line segment directed segment )

2. |2
XX' , YY' ZZ'
O
1
1
real line)
XX' , YY' ZZ'
X Y Z
X (x-axis) Y (y-axis) Z (z-axis)
O (origin) 2

3. |3
2
OX OY OZ X
positive x-axis) Y positive y-axis)
Z positive z-axis)
OX' OY' OZ' X
negative x-axis) Y negative y-axis)
Z negative z-axis)
X Y Z
3 4
3 4
X Y Z 3
• X Y

4. |4
XY XY
• X Z
XZ XZ
• Y Z
YZ YZ ( 5)
5
XY YZ XZ
8 XY
4 XY 4
octant)
6 X Y Z
1
( XY

5. |5
6
P
P P
(x,y,z)
x X P
YZ
YZ
P X
X
P YZ
y Y P
XZ
XZ
P Y

6. |6
y
P XZ
z Z P
XY
XY
P Z
Z
P XY x,y,z)
P
P(x,y,z)
P(x,y,z) z
XY Q(x,y,0)
P XY
R(0,y,z) P

7. |7
YZ S(x,0,z) P
XZ

8. |8

9. |9

10. |10

11. |11

12. |12

13. |13
“ ”

14. |14
1.
2.
3 4

15. |15

16. |16
“ ”
A

17. |17
= , =
ABCD
=
=
=

18. |18

19. |19

20. |20

21. |21
a b
a>
0 X a<
0 X
b>0
Y b<
0 Y
a,b ) x,y ) x+
a,y + b
)

22. |22
x,y,z
0) x,y,z )

23. |23

24. |24

25. |25

26. |26

27. |27
unit vector)
a
b
a
b
1 0
0 1
1
i
0
0
j
1

28. |28
MO = NO
i j
i =j
a
b a2 b2 c
c
a
b
c
a
1
b
a2 b2 c2
c
1 0 0
0 , 1 0
0 0 1
1 0 0
0 i 1 j 0 k
0 0 1

29. |29
Z
(0,0,
k (0,1, Y
j
1) i 0)
(1,0,
X 0)

30. |30

31. |31

32. |32

33. |33

34. |34

35. |35

36. |36

37. |37

38. |38

39. |39

40. |40

41. |41
5
www.samart.chs.ac.th
www.vector.th.gs
http://www.thaigoodview.com/library/contest2551/math04/16/2/
vector/index.htm