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Solved: Curve-plane intersections Find the points (if they
Chapter 13, Problem 46E(choose chapter or problem)
46-48. Curve-plane intersections Find the points (if they exist) at which the following planes and curves intersect.
\(y=1 ; \mathbf{r}(t)=\langle 10 \cos t, 2 \sin t, 1\rangle, \text { for } 0 \leq t \leq 2 \pi\)
Questions & Answers
QUESTION:
46-48. Curve-plane intersections Find the points (if they exist) at which the following planes and curves intersect.
\(y=1 ; \mathbf{r}(t)=\langle 10 \cos t, 2 \sin t, 1\rangle, \text { for } 0 \leq t \leq 2 \pi\)
ANSWER:Solution 46EStep 1 of 2:In this problem we need to find the points of intersection of the plane y = 1 , and the curve r(t) = , for 0 , provided it exists. Given ; plane is y = 1, and the curve r(t) = = From the curve we have , x = 10cos(t) , y = 2 sin(t) ,and z = 1.Now , the intersection of plane y = 1 ,and the curve r(t) = is ; 2 sin(t) = 1 sin(t) = t = = , , since 0 t 2 = , Therefore , t = , NOTE; If sin (x) = sin(y) , then x = ny , where n = zero or any integer.