Test: Vector Analysis - Electronics and Communication Engineering (ECE) MCQ

The surface ρ = 3, ρ = 5,  Ø = 100⁰  ,Ø = 130⁰ ,z = 3  and z = 4.5 define a closed surface. The enclosed volume is:

The surface ρ = 2, ρ = 4,  Ø = 45⁰  ,Ø = 135⁰ , z = 3  and z = 4 define a closed surface. The total area of the enclosing surface is:

The surface ρ = 3, ρ = 5,  Ø = 100⁰  ,Ø = 130⁰ , 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 = 2x² +y² - 2z² . 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 x²y + z = 3 and x ln z - y² = -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, 30⁰ , 60⁰ ) 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:

The curl of vector  is:

The curl of vector field 

The curl of vector field

  the value    is: