Question

91. Surface integral is used to compute :
(B​

Answer 1

.....…………….............,,,,,,,,,,

Answer 2

Explanation:

space. Thus, a curve is a function of a parameter, say t. Using the standard vector representations of

points in the three-dimensional space as r = (x, y, z), we can represent a curve as a vector function:

r(t) = (x(t), y(t), z(t))

or using the parametric equations x = x(t), y = y(t), and z = z(t). The variable t is called the

parameter.

Example 1.

1. Line. A line in space is given by the equations

x = x0 + at y = y0 + bt z = z0 + ct

where (x0, y0, z0) is a point on the line and

(a, b, c) is a vector parallel to it. Note that

in the vector form the equation r = r(0) + m t

for r(0) = (x0, y0, z0) and m = (a, b, c), has

exactly the same form as the well known y =

b + mx.

2. Circle in horizontal plane. Consider the

parametric equations x = a cost y =

a sin t z = b. Recall that the parametric equa-

tion of a circle of radius a centered in the origin

of the xy-plane are x = a cost, y = a sin t. Re-

call also that z = b represents the horizontal

plane passing b in the z-axis.

Thus, the equations

x = a cost y = a sin t z = b

represent the circle of radius a in the horizontal plane passing z = b on z-axis.

3. Ellipse in a plane. Consider the intersection of a cylinder and a plane. The intersection is

an ellipse. For example, if we consider a cylinder with circular base x = a cost, y = a sin t and

the equation of the plane is

1