Sketch the curve given in parametric form by r = ti+ sin tj + cos tk, 0 < t < 2π, and write down an integral to determine its length. Calculate the length of this curve. Write down a simple algebraic relation that determines a simple surface on which the curve lies. The length of this curve is: (a) 2√2 (b) 2π (c) 2√2 (d) π/2√√2 The surface on which the curve lies is: (i) a sphere x² + y²+z² = 1 (ii) a cylinder 2 + y² = 1 (iii) an elliptic cylinder (3x)2 + y² = 1 (iv) a cylinder y²+z² = 1 22

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