Consider the following. (1, 0, 1) 1 (0, 0, 0) (1, 0, 0), x (1, 1, 1) (a) Find a piecewise smooth parametrization of the path C shown in the figure. (0, 0, 0) to (1, 0, 0) r(t) = ti 0 ≤ t≤ 1 (1, 0, 0) to (1, 0, 1) r(t) = i+ tk 0 ≤t ≤ 1 (1, 0, 1) to (1, 1, 1) r(t) = i + tj + k 0 ≤ t≤1 (b) Evaluate 16x + y² z) ds. -z) ×

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Q: 11. Let F(x, y, z) = = (), and let P represent the path that follows the from (1, 0, 1) to (0, 1,0),…

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Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: C₁: r₁(s) C₂: r₂(t) C3 r3(u) = = = (s 2)i+ (2s² - 1)j + k 2t² i + (3t+7)j + (t+1) k (SER) (t = R)…

A: for the given vector functions for the curves C1,C2 and C3 To answer the given questions.

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Q: a) Compute the work done by F = (y², sin(z), x) along a straight line from (0,3,0) to (1, 0, 1). b)…

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