Divergence and Curl of a vector field are _________.
The two vector are R_{AM} = 20u_{x} + 18u_{y}  10u_{z }and R_{AN} = 10u_{x} + 8u_{y} + 15u_{z}. The u of the triangle that bisects the interior angle at A is:
The nonunit vector in the required direction is:
Two points in cylindrical coordinates are A(ρ = 5, Ø = 70^{0 }, z = 3) and B(ρ = 2, Ø = 30^{0 }, z = 1) A unit vector at A towards B is:
In cartesian coordinates:
The surface ρ = 2, ρ = 4, Ø = 100^{0} ,Ø = 130^{0} ,z = 3 and z = 4.5 define a closed surface. The enclosed volume is:
The surface ρ = 2, ρ = 4, Ø = 45^{0} ,Ø = 135^{0} , z = 3 and z = 4 define a closed surface. The total area of the enclosing surface is:
Area is:
The surface ρ = 3, ρ = 5, Ø = 100^{0} ,Ø = 130^{0} , z = 3 and z = 4.5 define a closed surface. The length of the longest straight line that lies entirely within the volume is:
A vector field H is:
A vector is A = yu_{x} +(x+z)u_{y} .At point P(2, 6, 3) A in cylindrical coordinate is:
The directional derivative of function φ = xy + yz + zx at point P(3, 3, 3) in the directiontoward point Q(4, 1, 1) is:
The temperature in a auditorium is given by T = 2x^{2} +y^{2}  2z^{2} . A mosquito located at (2, 2, 1) in the auditorium desires to fly in such a direction that it will get warm as soon as possible. The direction, in that it must fly is:
The angle between the normal to the surface x^{2}y + z = 3 and x ln z  y^{2} = 4 at the point of intersection (1, 2, 1) is:
The divergence of vector A = yzu_{x} + 4xyu_{y} + yu_{z} at point P(1, 2, 3) is:
The divergence of the vector at point P(1, 30^{0} , 60^{0} ) is:
Which of the quantities is nearest to the value of
The flux of over the closed surface of the cylinder 0 ≤ z ≤ 3 , ρ = 3 is:
By divergence theorem
The curl of vector is:
The curl of vector field
The curl of vector field
the value is:
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