The value of (∇ × A) at the point (1, 2, 3), where A = xy i - 2xz j + 2yz k, is:

If A = rnr, where r is the position vector, then ∇ · A is equal to:

Let vector F = 2xz î + 2x ĵ - y2 k̂. The value of the triple integral ∭V vector F dv, where V is the region bounded by x = 0, y = 0, x = 3, y = 8 and x2 ≤ z ≤ 6, is:

Find the directional derivative of φ(x,y,z) = 4xz3 - 3x2y2z at the point (2, -1, 2) in the direction of the vector 2i - 3j + 6k.