How can a vector be determined if it's rectangular components are known
Answers
A vector's resolution is called the process of splitting a vector. It would mean determining the effect of a vector in a specific direction in a simpler language. The parts of the vector that were obtained after the vector was split are known as Vector Components.
A vector's rectangular components: if a given vector's components are perpendicular to each other, they are called rectangular components.
Moreover, in the right – angled MONP,
cosθ=Ax/A
⇒ Ax = A cosθ … (1)Rectangular Componentssinθ=AyA
⇒ Ax = A sinθ … (2)
Squaring and adding equations (1) and (2) we get,
Ax² + Ay² = A² cos²θ + A² sin²θ = A² (cos²θ + sin²θ)
But, cos²θ + sin²θ = 1
∴ Ax² + Ay² = A²
⇒ A² = Ax² + Ay²
A=√Ax²+Ay²
This equation gives the vector's magnitude in terms of the magnitudes of the vector's components.
