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- Addition and Subtraction of Vectors

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## ADDITION AND SUBTRACTION OF VECTORS — GRAPHICAL METHOD

**Addition of Vectors:-**

(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