1. (a) Find parametric equations for the tangent line to the curve r(t) = ti + R

Question

1. (a) Find parametric equations for the tangent line to the curve r(t) = ti + R cos((pi)t)j + R sin((pi)t)k at the point (1, -R,0). (b) Sketch both the curve and the tangent line in part (a). Indicate with an arrow on the curve the dirction in which (t) increases. (If you are artistically challenged like me, describe in detail what your sketch should look like using English.) 2. (a) What is the fastest way to check that the parameter s in the vector equation of a psace curve r(s) is the arc length already? (b) Suppose you start at the point (0,0,3) and move 10 units of length along the curve x=3sin(t), y=4t, z=3cos(t) in the negative t-direction. Where are you now? 3. For each of the following space curves, (i) find parametric equations that represent the curve, using t as the parameter and (ii) find ds/dt where s stands for arc length. (a) the intersection curve of z=(4x^2+y^2)^(1/2) and y=3 (b) the intersection curve of z=(4x^2+y^2)^(1/2) and z=2.

Explanation / Answer

FOLLOW THIS T(t) is a parametric curve. According to Vector Calculus you must first derive the vector, to find the tangent vector. To derive the vector, you must derive each component. Since it is a 3D paramtetric curve and not a surface we derive each axis (x, y and z) So: r

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.