PCM
VECTORS
WHAT ARE THEY?
Quantities
Scalars
Quantities that can be solely or completely represented by thier values/ magnitudes and do not require any direction. *all these quantities follow normal math*
Vectors
Quantities that have:
-magnitude
-direction
-Follow special rules of mathematics.
Properties of Vectors
1. Representation of equality
2 vectors are said to be equal if they have the same magnitude and direction
The modulus of a vector and length, both represent its' magnitude.
5N
A
5N
B
not
5N
C
However, |A| = |B| = |C|
as all of thier magnitudes are the same.
2. Representation of vectors
Diagramatically
Head of the vector
Tail of the vector
Magnitude
Symbolically
(with direction)
V
(without direction)
|V|
3. Movement of Vectors
A vector can be moved parallel to itself anywhere in the universe without being changed.
4. Simple Multipilication
(+ve)
(-ve)
if a vector is multiplied with a positive number, only its magnitude is changed.
if a vector is multiplied with a negative number, only its direction is reversed.
X-1
5. ANGLE BETWEEN VECTORS
The smaller angle created when 2 vectors are joined either tail to tail or head to head is called the angle betweem vectors.
6. Triangle law of vectors
2
3
5
If two vectors are joined sucvh that the the head of the first vector touches the tail of the second vector, the resultant magnitude and direction will be given by a vector joining the tail of the first to the head of the second.
A + B = C
7. Polygon Law of vectors
If any number of vectors aree added in a way that the head of the first vector is touching the tail of the second vector, then the resultant is given by joining the tail of the first vector to the hehad of the last vector in the system.
Note:
if 'n' vectors make a closed polygon in order, the resultant is 0.
8. PARALELLOGRAM LAW
a
O
B
A
R
O
the angle between the vectors
a
the angle and direction of the resultant
R
Resultant Vector
tan
a
B sin
O
A + Bcos
O
R
2
A + B + 2ABcos