CHAPTER 2
FORCE VECTORS
Parallelogram Law
Vector addition
vector 
scalar: a positive or negative number
Vector substraction
Application in finding
Components of a Force
Resultant force
law of cosines: magnitude
Addition of Several Forces
law of sines: direction
law of sines: magnitudes of 2 force components
Multiplication or division of a vector by a scalar will change the
magnitude of the vector
negative scalar = change the sense of vector
Addition of a system of coplanar forces
A force is resolved into 2 components along x and y axes = rectagular components
= scalar notation
= Cartesian vector notation
: 
cos = ke/huyen
sin = doi/huyen ❗
Cartesian unit vector i and vector j
Coplanar Force Resultants
: 
components of resultant force
Pythagorean theorem
trigonometry
tan= doi/ke 🚩
Cartesian Vectors with Right-Handed Coordinate System
Rectangular Components of a Vector 
Cartesian Unit Vectors : 
OR 
(b/c of Cartesian Unit Vectors)
magintude 
❤
: 
direction 
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to solve problems in three
dimensions 🚩
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Position Vector r is fixed by 2 points
r = r AB (but NOT rA or rB)
Force Vector Directed Along a Line: F = F.u = F (r/r) 🚩
F (unit of force)
r (unit of length)
OR A = (A sin Φ cos θ) i + (A sin Φ cos θ) j + (A cos Φ) k 🚩 xem lai cong thuc nay
Because Az = A cos Φ
A' = A sin Φ
Then 
FIND THE ANGLE B/W 2 LINES/VECTORS
DOT PRODUCT = multiplying two vectors
A. B = A.B cosθ 🚩** ❤
IF 0° <= θ<= 180° 
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Laws of Operation
Communicative 
Multiplication by a scalar 
Distributive law 
Cartesian Vector Formulation
OR 
therefore 
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