💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

Problem 45 Medium Difficulty

Find a vector function that represents the curve of intersection of the two surfaces.

The hyperboloid $ z = x^2 - y^2 $ and the cylinder $ x^2 + y^2 = 1 $

Answer

$\mathbf{r}(t)=\cos t \mathbf{i}+\sin t \mathbf{j}+\cos 2 t \mathbf{k}, 0 \Leftrightarrow t=2 \pi$

More Answers

Discussion

You must be signed in to discuss.

Video Transcript

For this exercise, we have to find the vector function that represents the curve of intersection of two surfaces. And those surfaces are X squared plus y squared equals one a cylinder n z squared r Z equals x squared minus y squared. So since we know that co sign squared of theta plus sine squared of theta equals one, this implies that X equals co sign of T and why equals sanity? Then we can substitute this equation in for the Z equals X squared plus y squared here. So what we end up getting is that Z equals ico sine squared of T minus the sine squared of T, which is equal to co sign of two t Then that gives us the vector function that we're looking for, which is our f t equals co sign of T I flash sign he Jay plus co sign to t. K. Because we got this Z value from combining them. And we already determined the X and the Y values, which is r i n r j. Based on the fact, um, that we knew that coastline squared of data post sine squared of theta equals one