An infinite surface of linear current density $$K = 5{\widehat a_x}$$ A/m exists on the x-y plane, as shown in the figure. The magnitude of the magnetic field intensity (H) at a point (1, 1, 1) due to the surface current in Ampere/meter is ____________ (Round off to 2 decimal places).
The closed curve shown in the figure is described by
$$r = 1 + \cos \theta $$, where $$r = \sqrt {{x^2} + {y^2}} ;x = r\cos \theta ,y = r\sin \theta $$The magnitude of the line integral of the vector field $$F = - y\widehat i + x\widehat j$$ around the closed curve is ___________ (Round off to 2 decimal places).
A quadratic function of two variables is given as
$$f({x_1},{x_2}) = x_1^2 + 2x_2^2 + 3{x_1} + 3{x_2} + {x_1}{x_2} + 1$$
The magnitude of the maximum rate of change of the function at the point (1, 1) is ___________ (Round off to the nearest integer).
For a given vector $${[\matrix{ 1 & 2 & 3 \cr } ]^T}$$, the vector normal to the plane defined by $${w^T}x = 1$$ is