Are the following statements true or false? 1. The area vector of a flat, orient

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Are the following statements true or false? 1. The area vector of a flat, oriented surface is parallel to the surface. 2. If S| is the unit sphere centered at the origin, oriented outward and F = xi + yi + zk = r| than the flux integral _S F dA| is positive. 3. If Si is an open-ended circular cylinder centered about the z-axis. oriented away from the z-axis, and F = x, y, 0 |, then the flux of F| through S| is positive. 4. If S| is the unit sphere centered at the origin, oriented outward and the flux integral _S F dA| is zero, then F = 0|. 5. If S_1| is a rectangle with area 1 and S_2| is a rectangle with area 2, then 2 _S1 F dA = _s2 F dA| 6. If S| is the unit sphere centered at the origin, oriented outward and the flux integral _S F dA| is zero, then F(x, y, z)| is perpendicular to r = x, y, z | at every point of S|. 7. If S| is an open-ended circular cylinder centered about the z-axis. oriented away from the z-axis, and F = 3, -2,6 |, then the flux of F| through S| is zero. 8. If S| is the cube bounded by the six planes x = plusminus3| y = plusminus3| z = plusminus3|, oriented outward, and F = 2i - k|, then the flux of F| through S| is zero.

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