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A non - zero vector is parallel to the line of intersection of the plane determined by the vectors i, i +j and the plane determined by the vectors i - j, i + k. Then the angle between and the vector i - 2j + 2k is ,
The unit normal to the surface xy2 + 2xz = 4 at the point (2, -2, 3) is
The values of x for which the angle between the vectors is obtuse,
The value of line integral and C is the boundary curve of the upper half surface of the sphere x2 + y2 + z2 = 1.
The value of where F = 2xi + 3yj + 4zk and S is the surface of sphere x2 + y2 + z2 = 1
The differential equation of the family of parabolas with foci at the arigin and axis along the x-axis is)
Let y(x) = 4(x) sinx + v(x) cos x be a solution of the differential equation, y”+y sec x, Then 4(x) is
Let W be the region inside the solid cylinder x2 + y2 < 9 between the plane z = - 2 and the parabolio d z = x2 + y2. Let S is the boundary of W and be a vector field. Then the value of cannot be ?
If then at the point (1 -1 ,1 ), select the correct statements:
The value of line integral where C is the circle x2 + y2 = 16 , z = -1, is
if are unit vectors, then the possible values of is/are
The directional derivative of f at P in the direction of with
The value of for the vector field for a plane rectangular area with vertics at in x-y plane, is ____________.
The value of surface integral
Where S is closed Sufrace
Let S be the surface with the indicated orientaton then the value of
Let S be the portion of the cylinder y = Inx in the first octant whose projection parallel to the y-axis on to the xz-plane is the rectangle Rxz : Let be the unit vector normal to S that points away from the xz-plane. Let be a rector field, then the value of integral
The circulation of the field around the curve C in which the plane z = 2 meets the cone Counterclock wise as viewed from above, is equal to ....... (correct upto two decimal places)
The direcitional derivative of in the direction of the unit vector
Find the directional derivative of at the point
Find the derivation of in the direction v = 2i - 3j + 6k
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