Question
In: Math
Question: (a) Find parametric equations for the line of intersection of the planes given by 3x...
Question: (a) Find parametric equations for the line of
intersection of the planes given by 3x − 2y + z = 1 and 2x + y − 3z
= 3.
(b) Find the equation of the plane orthogonal to both of these
planes and passing through the point (−2, 1, 1).
Solutions
milcah answered 1 year agoRelated Solutions
Find the parametric equations of the line of intersection of the planes x − z =...
Find the parametric equations of the line of intersection of the
planes x − z = 1 and y + 2z = 3. (b) Find an equation of the plane
that contains the line of intersection above and it is
perpendicular to the plane x + y − 2z = 1.
Find a set of parametric equations for the tangent line to the curve of intersection of...
Find a set of parametric equations for the tangent line to the
curve of intersection of the surfaces at the given point. (Enter
your answers as a comma-separated list of equations.)
z = x2 +
y2, z = 16 −
y, (4, −1, 17)
Find a set of parametric equations for the tangent line to the curve of intersection of...
Find a set of parametric equations for the tangent line to the
curve of intersection of the surfaces at the given point. (Enter
your answers as a comma-separated list of equations.) z = sqrt(x2 +
y2) , 9x − 3y + 5z = 40, (3, 4, 5)
Find parametric equations for the tangent line to the curve with the given parametric equations at...
Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point.
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.$$ x=e^{-t} \cos t, \quad y=e^{-t} \sin t, \quad z=e^{-t} ; \quad(1,0,1) $$(b): Find the unit tangent vector \(\mathbf{T}\), the principal unit normal \(\mathbf{N}\), and the curvature \(\kappa\) for the space curve,$$ \mathbf{r}(t)=<3 3="" 4="" sin="" cos="" t="">$$
1. Given parametric equations below, find dy/dx , equations of the tangent and normal line at...
1. Given parametric equations below, find dy/dx , equations of
the tangent and normal line at the given point.
(a) x = t^2 , y = t^3−3t at t = 1
(b) x = cos(t), y = sin(2t) at t = π/4
2. ) Given parametric equations below, find d^2y/dx^2 and
determine the intervals on which the graph of the curve is concave
up or concave down.
(a) x = t^2 , y = t^3−3t
(b) x = cos(t), y...
Find the equation of the tangent plane and the parametric equations for the normal line to...
Find the equation of the tangent plane and the
parametric equations for the normal line to the surface
x2 + y2 - z = 0 at the point P(4,-1, 6).
Show all steps
Find a vector equation and parametric equations for the line. (Use the parameter t.) The line...
Find a vector equation and parametric equations for the line.
(Use the parameter t.)
The line through the point
(2, 2.9, 3.6)
and parallel to the vector
3i + 4j − k
r(t)
=
(x(t), y(t), z(t))
=
(a) Find parametric equations for the line through (3, 4, 8) that is perpendicular to the...
(a) Find parametric equations for the line through
(3, 4, 8)
that is perpendicular to the plane
x − y + 4z = 5.
(Use the parameter t.)
(x(t), y(t), z(t)) =
(b) In what points does this line intersect the coordinate
planes?
xy-plane
(x, y, z) =
yz-plane
(x, y, z) =
xz-plane
(x, y, z) =
1. Given parametric equations below, find the values of t where the the parametric curve has...
1. Given parametric equations below, find the values of t where
the the parametric curve has a horizontal and vertical
tangents.
a) x=t^2 - t, y= t^2 + t
b) x= e^(t/10)cos(t), y= e^(t/10)sin(t)
2. Find the arc length of the graph of the parametric equations
on the given intervals.
a) x= 4t+2, y = 1-3t , −1 ≤ t ≤ 1
b) x= e^(t/10)cos(t), y= e^(t/10)sin(t), 0 ≤ t ≤ 2π
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