# Addition and Subtraction of Vectors - Graphical Method

#### description

• Vector addition by rectangular components
• Graphical and analytical method
1. Triangle law of vector addition
2. Parallelogram law of vector addition
3. Polygon law of vector addition
• Subtraction of vectors

## ADDITION AND SUBTRACTION OF VECTORS — GRAPHICAL METHOD

(i) Only vectors of same nature can be added.
(ii) The addition of two vector A and B is resultant R
bar R = bar A + bar B and
 R= (A^2 +B^2 +2AB cos Θ)^(1/2) and
 tan β = (B Sin Θ)/(A + B Cos Θ)

Where Θ is the angle between vector A and vector B, And β is the angle which R makes with the direction of A.
(iii) Vector addition is commutative A + B = B+A
(iv) Vector addition is associative, A+ (B +C) = (A +B)+C
(v) R is maximum if Θ = 0 and minimum if Θ = 180 + 0.

Subtraction of two vectors:-
(i) Only vector of same nature can be subtracted.
(ii) Subtraction of B from A = vector addition of A and (-B),

Where  R= (A^2 +B^2 +2AB  Cos (180- Θ)^(1/2) and
 tan  β = (B Sin (180 - Θ))/(A + B Cos (180 - Θ))

Where Θ is the angle between A and B and β is the angle which R makes with the direction of A.
(iii) Vector addition is commutative A + B ≠ B+A
(iv) Vector addition is associative ,A+ (B +C ) ≠ (A +B )+C

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