Vector FunctionsLet x=f(t), y=g(t), z=h(t)be parametric equations that determine the path of a particle. Then rr(t)=φ(τ29ιρ+γ(τ29ϕρ+η(τ29κρis a position vector.Also, we can write rr(t)=ξιρ+ψϕρ+ζκρ.rr t( 29is a vector valued function.Domain:Range:The derivative of rr t( 29= rr(τ29 =φ(τ29ιρ+γ(τ29ϕρ+η(τ29κρ.The derivative of position is So r (t) =The derivative is also called the tangent vector. Speed is the magnitude of velocity so speed = v.
The second derivative of rr t( 29= rr(τ29 =φ(τ29ιρ+γ(τ29ϕρ+η(τ29κρ.The derivative of velocity is acceleration so rr(τ29 =αρτ( 29.ex. r(t) =t2, t3
Graphing rr(t), vrt( 29 ,αρτ( 291. r(t)is a position function with its tail at the origin and its head at the point f(t), g(t), h(t)().2. If you graph vt( )with its tail at the point f(t