Curve-plane intersections Find the points (if

Chapter 13, Problem 48E

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QUESTION:

46-48. Curve-plane intersections Find the points (if they exist) at which the following planes and curves intersect.

\(y+x=0 ; \mathbf{r}(t)=\langle\cos t, \sin t, t\rangle, \text { for } 0 \leq t \leq 4 \pi\)

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QUESTION:

46-48. Curve-plane intersections Find the points (if they exist) at which the following planes and curves intersect.

\(y+x=0 ; \mathbf{r}(t)=\langle\cos t, \sin t, t\rangle, \text { for } 0 \leq t \leq 4 \pi\)

ANSWER:

Solution 48EStep 1 of 3:In this problem we need to find the points of intersection of the plane y +x =0 , and the curve r(t) = , for 0 , provided it exists. Given ; plane is y+x =0, and the curve r(t) = = From the curve we have , x = cos(t) , y = sin(t) ,and z = t.NOw , the intersection of plane y +x =0 ,and the curve r(t) = is ; sin(t) + cos(t) = 1 sin(t) = - cos(t) = 1 = , , , since 0 t 4 Therefore , t = , , and NOTE; If tan (x) = tay(y) , then x = n , where n = zero or any integer.

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