Let are three arbitrary rector’s. Then the rector's are
The unit vector normal to the surface x2y + 2xz = 4 at the point (2,-2,3) is
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The derivative of f(x, y) at point (1, 2) in the direction of vector i + j is 2 √2 and in the direction of the vector - 2j is - 3 . Then derivative of f(x, y) in the direction - i - 2j is
The point at which the derivative of the function f(x,y) = x2 - xy - y + y2 vanishes along the direction is
Let where a is a constant. If the line integral over every closed curve c is zero, then a is equal to
Let denote the force filed on a particle traversing the path L from (0,0,0) to (1,1,1) along the cuive of intersection of the cylinder y= x2 and the plane z = x the work done by is
For a solenoidal vector field which of the following is not true ?
If S be the surface of sphere x2 + y2 + z2 = 9.
the integral is equal to
The value of surface integral over the surface of the paraboloid z = 1 - x2 - y2, z > 0, where
If the vector's satisfy the condition then is equal to
The line integral of the vector field, along the boundary of the triangle with vertices (1,0,0), (0,2,0), and (0,0,1), oriented anticlock wise, when viewed from the point (2,4,2) is
The value of integral
where C is the curve of intersection of the surface x2 + y2 + z2 = a2 bounded by the plane x + y + z = 0, is
The vector bisects the angle between the vectors then the unit vector along
Let T be the smallest positive real no. such that the tangent to the helix
at t = T is orthogonal to the tangent at t = π/2
Then the line integral of along the section of the helix from t = 0 to t = T is
Let c1 : x2 + y2 = 1 and be the curves from (-1,0,2) to (1,0,2) drawn counter clock wise in the lower half (y ≤ 0) of the plane z = 2 and let be a vector point function. Let the line integrals be then
Let S be the boundary of the region consisting of the parabolic cylinder z = 4 - x2 and the planes y = 0 , y = 2 and z = 0 and be a vector point function, then the value of is
The work clone by the force in moving a particle from the origin O ( 0 ,0 ,0 ) to the poin t D (1,1,0) on t h e z = 0 plane along the paths OABD as shown in the figure (where the coordinates are measured in meters) is,
If then calculate the flux of out of the region through the surface at z = c where region is bounded by -a ≤ x ≤ a, - b ≤ y ≤ b
The circulation of the field around the curve C where C is the intersection of the sphere x2+ y2 + z2 = 25 and the plane z = 3, is,
Let be a vector point function and S be an open surface x2 + y2 - 4x + 4z = 0 , z ≥ 0, Then the value of is equal to
Let and be a scalar function which satisfy Laplace eqn. Then the vector field is _______.
Let be a constant vector and then is equal to
If then the value of at the point (-1, 1, 1) is
Let is a unit vector, then for the maximum value of the scalar triple product will be equal to ?
Let there be two points A and B on the curve y = x2 in the plane OXY satisfying then length of the vector
Find equations for the tangent plane to the surface z = x2 + y2 at the point (2, -1, 5).
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