Parametric descriptions Give a parametric description of the form r ( u , v ) = 〈 x ( u , v ) , y ( u , v ) , z ( u , v ) 〉 for the following surfaces. The descriptions are not unique. Specify the required rectangle in the uv-plane . 11. The plane 2 x – 4 y + 3 z = 16
Parametric descriptions Give a parametric description of the form r ( u , v ) = 〈 x ( u , v ) , y ( u , v ) , z ( u , v ) 〉 for the following surfaces. The descriptions are not unique. Specify the required rectangle in the uv-plane . 11. The plane 2 x – 4 y + 3 z = 16
Parametric descriptionsGive a parametric description of the form
r
(
u
,
v
)
=
〈
x
(
u
,
v
)
,
y
(
u
,
v
)
,
z
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u
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〉
for the following surfaces. The descriptions are not unique. Specify the required rectangle in the uv-plane.
Describe and sketch the surface in double-struck R3 represented by the equation
y = 2x.
The equation represents the set of all points in double-struck R3 whose y-coordinate is ( insert answer) times their x-coordinate, that is,
{(x, 2x, z) | x is in double-struck R, z is in double-struck R}.
This is a vertical plane that intersects the xy-plane in the line
y = , z = .The portion of this plane that lies in the first octant is sketched in the figure.
QI: Find parametric equation s for the line through the point (0,1,2) that is parallel to the
plane x+y+z =2 and perpendicular to the line x=1+t, y=1-t, z=2t.
Q2: Find the distance between the following two planes:
P,: be the plane that passes through (0,-3,1) , (3,4,2)
(2,–1,-1)
P2: be the plane that pa sses through (-1,1,2) , (3,1,3) , (2,4,-1)
Q3: Show that if ū+v and ū-v are orthogonal then the vectors ū,v are of the same
length.
Q4. Find an equation of a plane that contains the line x=t, y=1+2t, z=2-t.
Sketch and identify the surface given by x? + 4y + 42² = 0.
University Calculus: Early Transcendentals (3rd Edition)
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