Del - Operator -I Starter Quiz

The directional directive of 4x²y + z³ at (1, 2, 1) in the direction of is

The vector function represented by F = a_x(5y – k₁z) + a_y (3z + k₂x) + a_z (k₃y – 4x) represents a conservative field, where a_x, a_y & a_z represents unit vectors along the x, y, & z-axis respectively. Find the values of k₁, k₂ & k₃ = ?

The divergence of the vector field at (1,1,1) is

Divergence of the vector field

The curl of vector field (x, y, z) = x² + 2z – y is:

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