## Related questions with answers

Question

Find the parametric equations of the line that is tangent to the curve of intersection of the surfaces $x=z^2$ and $y=z^3$ at (1,1,1).

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 4Given $f\left(x,y,z \right)=x-z^{2}=0$ and $g\left(x,y,z\right)=y-z^{3}=0$

$\begin{align*} \nabla f\left(x,y,z \right)&=\dfrac{\partial f\left(x,y,z \right)}{\partial x}\hat{i}+\dfrac{\partial f\left(x,y,z \right)}{\partial y}\hat{j}+\dfrac{\partial f\left(x,y,z \right)}{\partial z}\hat{k} \\ &=\hat{i} -2z\hat{k} \\ \nabla f\left(1,1,1 \right)&=1\hat{i} -2\hat{k}\end{align*}$

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