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WZ
Numerade Educator

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Problem 32 Medium Difficulty

At what points does the helix $ r(t) = \langle \sin t, \cos t, t \rangle $ intersect the sphere $ x^2 + y^2 + z^2 = 5 $?

Answer

$\begin{array}{ll}t=2 & \left(\sin ^{2}, \cos ^{2} ,2\right) \\ t=-2 & \left(\sin ^{-2} \cos ^{-2},-2\right)\end{array}$

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Video Transcript

The problem is at the board points as a Alex I Ke a sicko, too sci fi scientist and the teeth intersected. This fear exploited plus y square. Plus the square is they're going to fly off. So from this curve with half axe physical science, why is he going to assign you? Thing is they control on by the relations X square plus y square. Stay square. You go too far. We have signed you squared plus sign. He squired past the square. It's the code five. This's It would want one past the squire. It's equal five. He is equal to class or minus two. So when he is equal to the point is signed. We signed to consign two on two. He's the connective, too. Point is sign Negative too. Consign! Negative to Andi. Negative two. So I had to the point signed to assign to two. What is the point sign next to assign it to me, too. The Halifax intersected. Sophy