Understanding vector calculus For the following questions do not perform any calculations. You may, if you like, include sketches: 1. Explain why the line integral of F = yi + xj around any unit circle is zero. 2. Given the vector eld (i + j) ,I' i. /x + y, explain why the line integral of it around an arbitrary closed contour in the (x, 3;) plane may not be zero even though it is a conservative field. 3. Explain why for the cylindrical surface x2 + y2 = 1, 1 <_: z ffs de="D;" ff5 is="0,-" d5="471'." in part conser theform ofthe unit normal to this surface courtesirm coordinates marks>