Considere a uma curva regular e simples $\mathcal{C}$ \mathcal{C} em $\mathbb{R}^3$ \mathbb{R}^3 parametrizada por
$(x(t),y(t),z(t))=(\sqrt{4-5t},2t,t), \ \ t\in [-\frac{2}{5},\frac{2}{5}]$ (x(t),y(t),z(t))=(\sqrt{4-5t},2t,t), \ \ t\in [-\frac{2}{5},\frac{2}{5}].
Indique qual/quais as possíveis equações vetoriais da reta tangente a $\mathcal{C}$ \mathcal{C} no ponto (2,0,0).

Question

Considere a uma curva regular e simples $\mathcal{C}$ \mathcal{C} em $\mathbb{R}^3$ \mathbb{R}^3 parametrizada por

$(x(t),y(t),z(t))=(\sqrt{4-5t},2t,t), \ \ t\in [-\frac{2}{5},\frac{2}{5}]$ (x(t),y(t),z(t))=(\sqrt{4-5t},2t,t), \ \ t\in [-\frac{2}{5},\frac{2}{5}].

Indique qual/quais as possíveis equações vetoriais da reta tangente a $\mathcal{C}$ \mathcal{C} no ponto (2,0,0).

Accepted Answer

(x,y,z)=(2,0,0)+\lambda (-\frac{5}{4},2,1), \ \ \lambda \in \mathbb{R}

Accepted Answer

(x,y,z)=(2,0,0)+\lambda (5,-8,-4), \ \ \lambda \in \mathbb{R}

Answer

(x,y,z)=(2,0,0)+\lambda (5,-3,-2), \ \ \lambda \in \mathbb{R}

Answer

(x,y,z)=(\frac{3}{4},2,1)+\lambda (-\frac{5}{4},2,1), \ \ \lambda \in \mathbb{R}

Answer

(x,y,z)=(2,0,0)+\lambda (\frac{1}{4},2,1), \ \ \lambda \in \mathbb{R}

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