Vecter & scalar

F
F F

F F
F F F F F 2
F F
1. F ( Scalar quantity ) F F F F F
F F F F
F
2. F ( Vector quantity ) F F
F F F F F F
F F F
2.1 F F F
F F
v
v 3 F C
A
v 3 F
2 F B θ
v v v
1. F A,B C
v
FA 2 F
v
FB 3 F
v
FC 3 F θ
2.2 F F F2 F F F
2. v
A v
v v 2 F D v v
C = D
A = B 2 F 3 F
3 F
v v
B C
2. F F
2.3 F F F2 F F F F F
3. v v
v C F D
A v 3 F
v
A F
v
B 2 F D v
2 F 3 F -D
v 3 F
B v
v v
A = -B 2 F C
v v v
-B C = -D

2.4 F
F F F F2
2.4.1 F F F F F
F F F F
F F
v
v D
v B v
C
A

v v v v
1. F F A +B+C+D

v v v v
2. F F A -B+C-D

v v v v
3. F F B-C +D-A

2.4.2 F F F F F F
F F F F F F
F F
F F F
F 2 F F
v v v
FA B θ F F( R ) F
F

F F
v
B
v
A θ

v
By v
v B 1.
v
B F
v
FR
R
θv
v
A Bx
v v v v v v
R = A+B , FB F BX , BY
v v v v
F R = A + BX+ BY

v B sin θ
R v
B v
2. F FR F F
θ
v B cos θ
A
F F
R= ( A + B cosθ ) 2 + ( B sin θ ) 2
R= A 2 + 2AB cos θ + B 2 cos 2 θ + B 2 sin 2 θ
R= A 2 + 2AB cos θ + B 2 ( cos 2 θ + sin 2 θ )
F cos2θ + sin2θ = 1 , R= A 2 + 2AB cos θ + B 2
F F F F2 F F

R= A 2 + B 2 + 2AB cos θ ******

v v
F FR F F F FR α

R B sin θ
B
α θ
A B cos θ
v
F FR F α
F F
tan α =
F
B sin θ
F tan α = *****
A + B cosθ

v v
F F F A 4 F B 3 F F
F 0 , 60 , 90 180 F

v v
A 4 F B 3 F F 0

F v v v
B A 4 F B 3 F
v
A v
R 7 F

R= A 2 + B 2 + 2AB cos θ , F θ=0
R= A 2 + B 2 + 2AB cos 0° , cos 0° = 1
R= A 2 + B 2 + 2AB , ( A + B )2 = A2 + 2AB +B2

v v
A 4 F B 3 F F 60
F v
B v v
R B 3 F
60° 60°
v v
A A 4 F

R= A 2 + B 2 + 2AB cos θ , F θ = 60
1
F R= A 2 + B 2 + 2AB cos 60° , cos 60° =
2

v v
A 4 F B 3 F F 90
F v v
v R B 3 F
B
90° 90°
v v
A A 4 F

R= A 2 + B 2 + 2AB cos θ , F θ = 90
F R= A 2 + B 2 + 2AB cos 90° , cos 90° = 0

v v
A 4 F B 3 F F 180

F v v v
B A 4 F B 3 F
v
A v
R 1 F

R= A 2 + B 2 + 2AB cos θ , F θ = 180
R= A 2 + B 2 + 2AB cos 180° , cos 180° = -1

F F F F FF
1. F2 F 0..F
F F F (R = A + B)

2. F2 F F F 180..
F F F (R = A - B)

3. F2 F F θ
F F F R= A 2 + B 2 + 2AB cos θ

4. F2 F F 90
F F F R= A 2 + B2

Vecter & scalar

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