Vectors - Derivation of Subtraction Formula

Description:

Magnitude of the resultant vector (Formula)

For subtraction, S→ = a→ − b→, replace ′θ′ with ‘(π − θ)′

D = √a² + b² + 2abcos(π - θ)

This implies, D = √a² + b² + 2abcos(π - θ) [because cos(π − θ) = − cos(θ)]

Direction of the Resultant Vector (Formula)

For subtraction, S→ = a→ − b→, replace ′θ′ with ‘(π − θ)′

tan α = b sin(π - θ)/a + b cos(π - θ)

This implies, tan α = b sin θ/a - b cos θ [because cos(π − θ) = − cos(θ)]

[IMPORTANT NOTE: Sign Convention must be taken carefully]