Problems on vector calculus || Achievers Quiz 1

For a scalar function F(x,y,z,) = x² + 3y² + 2z², the gradient at the point P (3,2,1) is

For the scalar field
u = the magnitude of the gradient at the point (1, 3) is :

Given a vector field

If the vector field  is solenoidal, then the value of k will be

A vector is given by  The divergence of vector at x = 1 is:

F(x, y) = (x² + xy). It’s line integral over the straight line from (x, y) = (0, 2) to (x, y) = (2, 0) evaluates to