Vectors | Digital Notes
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Why do we need vectors?
- Physical quantity(PQ) = nu
where n is the magnitude and u is the unit.
Difference between scalor quantities and vector quantities?
Scalor Quantity
- 1)Numerical Value only
- 2)Added according to ordinary rules of algebra.
Examples:Mass distance,speed,Tempratur,Energy
Vector Quantity
- 1)
- a)Numerical value(Magnitude)
- b)Direction
- c)obeys vector law of addition(Necessary condition to ve a vector).
- 2)Added according to Vector law of addition.
Examples : Displacement,Velocity,force,Accleration.
Note: All Vector quantities have direction BUT All quantities that have direction are not vectors.
Representation of vectors
Representation of vectors imageImportant points of vector
Important points related to vector imageTypes of Vector
- Equal Vector
- Negative Vector
- Parallel Vector
- Collinear Vector
- Coplanar Vector
- Concurrent Vector
- Unit Vector
- Zero/Null Vector
Methods of Vector Addition
1.Graphical Method or Geometrical Method
2.Analytical Method
Graphical Method of Vector Addition
1.Triangle Law
2.Parallelogram Law
3.Polygon law
Vector Addition obeys Commutative law
Vector Addition is Associative
Analytical Method of Vector Addition
- Magnitude of Resultant |R| & Direction of Resultant
R2 = A2 + B2 + 2AB Cosθ
-Direction
Tan(alpha) = Bsinθ ÷ A + Bcosθ
Vector Addition Special Cases:-
Case 1: (theta) = 0 [ R = A + B ] max.
value of resultant.
Case 2: (theta) = 180 [ R = A - B ] min.
value of resultant.
Case 3: (theta) = 90 [ R = √A2 + B2]
Subtraction of Vectors | Derivative of formula
|R| = √A2 + B2 - 2ABCosθResolution of Vector
Unit Vector
A unit vector is a dimensionless vector having a magnitude of exact 1 and it
gives direction.
Orthogonal Unit Vector : i^,j^,k^(mutually perpendicular)
î----unit vector in +x - direction
ĵ----unit vector in +y - direction
^k----unit vector in +z - direction
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