Match the equation with its graph. r(u, v) = u cos(v) i + u sin(v) j + v k
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Determine which families of grid curves have u constant and which have v constant.
u constant
each grid curve lies in a plane z =
ky that includes the x-axis
the grid curves lie in the vertical plane y =
(tan (u))x
each grid curve is a circle of radius |u| in the horizontal plane z =
sin(u)
each grid curve is a vertically oriented circle
each grid curve is a circle of radius (1 - Ju|) in the horizontal plane z = u
each grid curve is a helix
v constant
each grid curve is a circle contained in the vertical plane x =
sin(v) parallel to the yz-plane
the vertical planes y
= kx through the z-axis
O a straight line in the plane z = v which intersects the z-axis
the grid curves run vertically along the surface in the planes y = kx
the grid curves are the spiral curves
O the grid curves lie in a horizontal plane

Transcribed Image Text:Match the equation with its graph.
r(u, v) = u cos(v) i + u sin(v) j + v k
ZA
OI
OII
ZA
ZA
OIV
OII
Ov
OVI
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