b-) Find the point closest to the origin on the intersection curve of the 2² =...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylinder -+ y1 and the plane z - 2y -7. Use s as the arc-length parameter with s 0 corresponding to the point (0, 1,9) oriented counter-clockwise as seen from above.
#48
#46
and #48
In Exercises 39-48, find a parametrization of the curve. 39. The vertical line passing through the point (3,2,0) 40. The line passing through (1,0,4) and (4.1.2) 41. The line through the origin whose projection on the xy-plane is a line of slope 3 and whose projection on the yz-plane is a line of slope 5 (ie, Az/Ay = 5) 42. The circle of radius 1 with center (2, -1, 4) in a plane parallel to the...
3. What point on the line y = 7 - 3x is closest to the origin? a. Sketch the line carefully and mark the point on the line that you think is closest to the origin. b. Write the distance between the origin and a point (x,y) in the plane. If you don't know, think of a triangle with base x and height y. 8 7 6 c. The point must be on the line, so you can write the...
vectors. Need help with those questions please
1a). In three-space, find the intersection point of the two lines: (x, y, z) = (-1,2,0] + [3,-1, 4) and [x, y, ) = -6, 8, -1] + [2,-5, -3). b) Determine a direction vector in integer form of the line of intersection of the two planes 2x + 2y+2-12-0 and (x, y, z)=(2,0,0]+${1,2,0]+(1.0,-2) [2,3] 2. What is the distance between the point (-81) and the plane 5x-2-2y+52 [2] 3. Find the point(s)...
Consider the paraboloid z=x2+y2. The plane 2x−2y+z−7=0 cuts the paraboloid, its intersection being a curve. Find "the natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your...
Question 3 3 pts Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The cone z = V x2 + y2 and the plane z =6+y 12 1 12 a. r= 1 (61,42 – 36,42 +36) b. 1) = 1 (12t,t2 + 36,42 +36) +(12t,– 12,42 +12) ${12t,t2 – 36,2 +36) P(8) = 1 / 2 C. d. (6) 2 1
Find a vector func The cone ction, r), that represents the curve of intersection of the two surfaces. z-r +y2 and the plane z 8 +y a. r()-i+ (0.03125t-8)j+ (0.03125t +8)k b. r(t)-i+ (0.0625t +16)j+ (0.0625t2 +16)k c. r r) i (0.0625t-16)j+(0.0625t2 +16)k d. r()-i+ (0.0625t-16)j+ (0.0625f2 +16)k
Find a vector func The cone ction, r), that represents the curve of intersection of the two surfaces. z-r +y2 and the plane z 8 +y a. r()-i+ (0.03125t-8)j+ (0.03125t +8)k b....
(1 point) Consider a right circular solid cone S standing on its tip at the origin. The height of the cone is 3 and the radius of the top is 8. Find the centroid of the cone by following the steps below. Assume the density of the cone is constant 1. a. The mass of the cone is m Jls 1 d(x, y, 2) b. Let Q(2) be the disk that is the intersection of the cone with the horizontal...
Find the point on the plane x - 2y ^ 3 * z = 6 that is closest to the point (0, 1, 1) .
how do you find the coordinates of the point (x, y, z) on the plane z = 1 x + 1 y + 2 which is closest to the origin