VECTORS

1. Vectors subtraction and
multiplication

2. CONCEPTS
• revision on VECTORS addition
• Vectors subtraction
• Vectors multiplication
• Vectors in three dimentionds

11. Vectors multiplication

12. • Why we use vectors multiplication ?
To define the magnitude of there product
Like >>>
Work = displacement * force

21. Vectors in 3D

22. nD Space
nD Space: n (typically)
n : number of dimensions
Examples:
• 1D space: time, along a line or curve
• 2D space: plane, sphere
• 3D space: the world we live in
• 4D space: 3D + time
H&B A-2

23. 3D coordinates 1
3D Cartesian coordinates:
x
y
(x,y,z)
Right-handed Left-handed
H&B A-1
z
x
y
(x,y,z)z

24. 3D coordinates
Cylinder coordinates:
x
y
(x,y,z)
H&B A-1
z

zz
ry
rx





sin
cos