A field is given as G = [25/(x2 + y2)](xax + yay ). Find (a) a unit vector in the direction of G at P(3, 4, −2); (b) the angle between G and ax at P; (c) the value of the following double integral on the plane y = 7.
2. By expressing diagonals as vectors and using the definition of the dot product, find the smaller angle between any two diagonals of a cube, where each diagonal connects diametrically opposite corners and passes through the center of the cube.
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