Consider the vector field F(x, y, z) = y cos (xy) i + x cos (xy)...

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Consider the vector field F(x, y, z) = y cos (xy) i + x cos (xy) j — sin zk. (i) Calculate the curl of the vector field F. State whether F is conservative. (ii) Let C be the curve joining the origin (0, 1, −1) to the point with coordinates (1,2√2,2) defined by the following parametric curve In t In 2 Calculate the scalar line integral of the vector field. [F r(t) = · dr. 3 i+tžj+t costk, 1 ≤ t ≤ 2. Consider the vector field F(x, y, z) = y cos (xy) i + x cos (xy) j — sin zk. (i) Calculate the curl of the vector field F. State whether F is conservative. (ii) Let C be the curve joining the origin (0, 1, −1) to the point with coordinates (1,2√2,2) defined by the following parametric curve In t In 2 Calculate the scalar line integral of the vector field. [F r(t) = · dr. 3 i+tžj+t costk, 1 ≤ t ≤ 2.