Vector-valued functions Find a function r(t) that describes the following curve. A circle of radius 3 centered at (2, 1, 0) that lies in the plane y=1

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Vector-valued functions Find a function r(t) that describes the following curve.  A circle of radius 3 centered at (2, 1, 0) that lies in the plane y=1

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Step 1 Given: A circle of radius 3 centered ate (2, 1, 0) that lies in the plane y=1 To Find: Vector-valued function r(t) that describes the above curve. Formula Used: The equation of a circle with radius rand center (a, b, c) is given by: (x−a)2+(y−b)2+(z−c)2=r2 Step 2 Calculations: The equation of the circle with radius 3 centered at (2, 1, 0) is given by: (x−a)2+(y−b)2+(z−c)2=32=9 The circle lies in the plane y=1 ⇒ The equation of circle passing through y=1 is given by: (x−2)2+(z−0)2=9 To find the vector valued function r(t), find the set of parametric equations: x−2=3cos⁡t⇒x=2+3cos⁡ z−0=3sin⁡t⇒z=3sin⁡ Hence, &amp;lt;x,y,z≥&amp;lt;2+3cos⁡t,1,3sin⁡t&amp;gt; The vector valued function is therefore given by: r(t)=&amp;lt;2+3cos⁡t,1,3sin⁡t≥(2+3cos⁡t)i+j+(3sin⁡t)k Step 3 Answer: r(t)=(2+3cos⁡t)i+j+(3sin⁡t)k

Vector-valued functions Find a function r(t) that describes the following

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