vector field

Given F = a_x(3y + k_1z) + a_y(k_2x - 2z) + a_z(k_3y – x), where a_x, a_y and a_z are the unit vectors in Cartesian coordinate system. The product k_1k_2k_3 for which F is irrotati...

The closed curve shown in the figure is described by r = 1 + cosθ, where r = √x² + y²; x = rcosθ, y = rsinθ The magnitude of the line integral of the vector field F = -yî + xĵ arou...

If A = 2xi + 3yj + 4zk and u = x² + y² + z², then div(uA) at (1, 1, 1) is _________.

The line integral of the vector field $$\,\,F = 5xz\widehat i + \left( {3{x^2} + 2y} \right)\widehat j + {x^2}z\widehat k\,\,$$ along a path from $$(0, 0, 0)$$ to $$(1,1,1)$$ param...

Divergence of the three-dimentional radial vector field $$\overrightarrow F$$ is

$$$F\left(x,y\right)=\left(x^2\;+\;xy\right)\;{\widehat a}_x\;+\;\left(y^2\;+\;xy\right)\;{\widehat a}_y$$$. Its line integral over the straight line from (x, y)=(0,2) to (2,0) eva...