9_VectorFunc - Vector Functions Let x f(t y g(t z h(t be parametric equations that determine the path of a particle r r r f(t)i g(t j h(t)k is a

# 9_VectorFunc - Vector Functions Let x f(t y g(t z h(t be...

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Vector Functions Let x = f ( t ), y = g ( t ), z = h ( t ) be parametric equations that determine the path of a particle. Then r r ( t ) = φ ( τ 29 ι ρ + γ ( τ 29 ϕ ρ + η ( τ 29 κ ρ is a position vector. Also, we can write r r ( t ) = ξι ρ + ψϕ ρ + ζκ ρ . r r t ( 29 is a vector valued function. Domain: Range: The derivative of r r t ( 29 = r r ( τ 29 = φ ( τ 29 ι ρ + γ ( τ 29 ϕ ρ + η ( τ 29 κ ρ . 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 r r t ( 29 = r r ( τ 29 = φ ( τ 29 ι ρ + γ ( τ 29 ϕ ρ + η ( τ 29 κ ρ . The derivative of velocity is acceleration so r r ( τ 29 = α ρ τ ( 29 . ex. r ( t ) = t 2 , t 3
Graphing r r ( t ), v r t ( 29 , α ρ τ ( 29 1. 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 v t ( ) with its tail at the point f ( t