Vector Calculus - 8 - Mathematics MCQ

The value of  along the circle x² + y² = 1 is  

The value of  is

Directional derivative of ψ(x,y,z) = xy² + 4xyz + z² at the point (1, 2, 3) in the direction of  is 

If  and  are two vectors then the value of will be

The value of div grad Φ is

The value of  is

Gauss’s divergence theorem is

If   then the value of div  will be

Let W be the region bounded by the planes x = 0, y = 0, y = 3, z = 0 and x + 2z = 6. Let S be the boundary of this region. Using gauss’ divergence theorem, evaluate, where and ň is the outward unit normal vector to S. 

If  is a differentiable vector point function, then the value of div curl  is 

Let  and 
Q. The unit vector perpendicular to the plane containing  and  is

Let us consider the scalar point function f(x y, z) =x² + y² + z²
Q. The grad of f(x, y, z) is

Let us consider the scalar point function f(x y, z) =x² + y² + z²
Q. The directional derivative of f(x, y, z) at the point P(1, 1, 1) along  is

Let where a, b and c are constants and S is the surface of unit sphere.
Q. The value of is

Let where a, b and c are constants and S is the surface of unit sphere.
Q. The value of is

 A vector normal to  is

If  and curve C is the arc of the curve y = x³ from (0,0) to (2,8), then the value of