Try the fastest way to create flashcards
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

Verified
Step 1
1 of 4

Given $f\left(x,y,z \right)=x-z^{2}=0$ 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*}

## Recommended textbook solutions #### Calculus

9th EditionISBN: 9780131429246Dale Varberg, Edwin J. Purcell, Steve E. Rigdon
6,552 solutions #### Thomas' Calculus

14th EditionISBN: 9780134438986 (11 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,142 solutions #### Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (6 more)James Stewart
11,085 solutions #### Calculus: Early Transcendentals

9th EditionISBN: 9781337613927 (1 more)Daniel K. Clegg, James Stewart, Saleem Watson
11,050 solutions