1. Write and explain the vector equation for a curve in 3 dimensions. Use graphs to...

 

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1. Write and explain the vector equation for a curve in 3 dimensions. Use graphs to illustrate your understanding. 2. Write the parametric equations for a curve in 3 dimensions. Explain the connection between parametric equations and vector equations. 3. Sketch the curve for 0 ≤ t ≤ 2n: r(t) =< 3 cos (t), -2 sin(t) > 4. Find a vector function that describes the curve of intersection of the cylinder x² + y² = 4 and the plane x + y + 2z = 4. Also graph these using GeoGebra. 5. Find the curvature of the following curve: f(t) =< t, 1t²t² > 1. Write and explain the vector equation for a curve in 3 dimensions. Use graphs to illustrate your understanding. 2. Write the parametric equations for a curve in 3 dimensions. Explain the connection between parametric equations and vector equations. 3. Sketch the curve for 0 ≤ t ≤ 2n: r(t) =< 3 cos (t), -2 sin(t) > 4. Find a vector function that describes the curve of intersection of the cylinder x² + y² = 4 and the plane x + y + 2z = 4. Also graph these using GeoGebra. 5. Find the curvature of the following curve: f(t) =< t, 1t²t² >