$$A$$ vector is defined as $$f = y\widehat i + x\widehat j + z\widehat k\,\,$$. Where $$\widehat i,\widehat j,$$ and $$\widehat k$$ are unit vectors in cartesian $$(x, y, z)$$ coordinate system. The surface integral - -over the closed surface $$S$$ of a cube with vertices having the following coordinates: $$(0,0,0), (1, 0, 0), (0, 1, 0), (0,0,1), (1, 0, 1), (1,1,1), (0, 1, 1), (1, 1, 0)$$ is _______.

For a vector $$E,$$ which one of the following statements is NOT TRUE?

A sphere of unit radius is centered at the origin. The unit normal at a point $$(x, y, z)$$ on the surface of the sphere is the vector.

If a vector $$\overrightarrow R \left( t \right)$$ has a constant magnitude then