Parametrize a path for the curve that is a circle in the x-y plane that has radius 2 (a) with center (0, 0) going counterclockwise (b) with center (1, 2) going counterclockwise (c) with center (1,2) going clockwise (d) Now modify this to be a path in 3 dimensional space, for a circle "above" the xy plane with a height of z = 3, with center (1,2,3), and moving counterclockwise as we look down from the positive z-axis. Hint: just set z = 3 and compute the other coordinates as in prior examples. (e) Find the formula for a helix that is found on a standard toilet roll interior (hard to come by?): Use centimeters for units. Note that the diameter is 4.2cm, and the height is 11.4cm, and the number of revolutions of the helix is 1 and 1/8th, i.e. 1.125.

Q: For each of the exercises in this chapter, give a parametric description of the curve, and then…

A:

Q: Integrate counterclockwise dz, C the circle with z2 + 12z + 35 center –5 and radius 2. dz z2 + 12z +…

A:

Q: Find foF dr where C is a circle of radius 3 in the plane x+y+z= 8, centered at (1, 3, 4) and…

A:

Q: The parametric equations I= 11 + (I2- 1)t, y=y+ (y2- y1)t where 0<t< 1 describe the line segment…

A:

Q: For each of the exercises in this chapter, give a parametric indicating the direction it is traced…

A: Introduction: A parametric equation is one in which the dependent variables are defined as…

Q: Determine an equation for the plane that's tangent to the surface z = 6x2 + 7y2 at point (-3, -2,…

A:

Q: Find an equation of the plane that contains point A(5,1,1) and the line that is given with…

A: Please see the below picture for detailed solution.

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y? = 8,…

A: Given: The parametric equations for the line tangent to curve of intersection of the surfaces…

Q: Consider two non-parallel lines L1 and L2 in R2 with the following parametric equations: (3,6) +…

A: Given : L1 = (3, 6) + s(3, -4) and                   L2 = (-4, -6) + t(2, -4)

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: What is the equation of the plane passing through the point (2, -3, 1) and perpendicular to the line…

A: A plane is a two-dimensional flat surface that extends indefinitely in all directions. It is…

Q: Li Syaoran is riding an airplane which departs from an airport located at (360, 0) miles in the…

A: The westward speed of the airplane = 480 miles/ hour The northward speed of the airplane = 120…

Q: Find a parametric equation of a line that passes through the point (1,3,-4) and is perpendicular to…

A: To find a parametric equation of a line that passes through the point 1, 3, -4 and is perpendicular…

Q: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

A:

Q: Find the distance between the skew lines with parametric equations x=3+t, y=2+6t, z = 2t, and…

A: Given :x=3+ty=2+6tz=2tx=2+2sy=4+14sz=-2+5s

Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

A:

Q: Parametrize the circle of radius 7 centered at (-2, 3) in the clockwise direction starting at…

A: Here I am attaching image so that you understand each and every step.

Q: The locus of the foot of the perpendicular from the centre of the hyperbola xy = c² on a variable…

A: Given hyperbola equation is  xy = c2 The parametric form of this hyperbola is  x = c t  and   y =…

Q: Does the plane x = 5 have a trace in the yz-plane? Explain.

A: Given: The plane is: x=5 We have to determine the given plane is trace in the yz-plane and explain