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Addition and Subtraction of Vectors — Graphical Method

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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

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